A automobile factory makes cars and pickup trucks.It is divided into two shops, one which does basic manu- facturing and the other for finishing. Basic manufacturing takes 5 man-days on each truck and 2 man-days on each car. Finishing takes 3 man-days for each truck or car. Basic manufacturing has 180 man-days per week available and finishing has 135.If the profits on a truck are $300 and $200 for a car.how many of cach type of vehicle should the factory produce in order to maximize its profits?What is the maximum profit? Let be the number of trucks produced and za the numbcr of cars.Solve this sraphically
Answers
The maximum profit is $13,500, which is obtained when the factory produces 0 trucks and 67.5 cars (or 68 cars, since we can't produce fractional cars).
Let's solve the given problem graphically: Let 'x' be the number of trucks and 'y' be the number of cars.
Let's first set up the objective function:
Z = 300x + 200y
Now let's set up the constraints:
5x + 2y ≤ 180 (man-days available in Basic Manufacturing)
3x + 3y ≤ 135 (man-days available in Finishing)
We also know that x and y must be non-negative.
Therefore, the LP model can be formulated as follows:
Maximize Z = 300x + 200y
Subject to: 5x + 2y ≤ 180
3x + 3y ≤ 135
x, y ≥ 0
Now, let's plot the lines and find the region that satisfies all the constraints:
From the above graph, the shaded region satisfies all the constraints. We can see that the feasible region is bounded by the following vertices:
V1 = (0, 0)
V2 = (27, 0)
V3 = (22.5, 15)
V4 = (0, 67.5)
Now let's calculate the value of Z at each vertex:
Z(V1) = 300(0) + 200(0)
= $0
Z(V2) = 300(27) + 200(0)
= $8,100
Z(V3) = 300(22.5) + 200(15)
= $10,500
Z(V4) = 300(0) + 200(67.5)
= $13,500
Therefore, the maximum profit is $13,500, which is obtained when the factory produces 0 trucks and 67.5 cars (or 68 cars, since we can't produce fractional cars).
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Related Questions
What is the missing angle? (Please use image attached)
Answers
Answer:
56
Step-by-step explanation:
Since vertical angles are equal, we know the two angles labeled are equal.
We can then set up an equation to get
\(19x-28=9x+52.\)
Subtracting \(9x\) from both sides to isolate the variable gives us
\(10x-28=52\).
Then, adding \(28\) to both sides gives
\(10x=80,\)
and dividing both sides by 10 gives
\(x=8.\)
Now, we can find the measure of \(9x+52\) by plugging what we found for \(x\) in:
\(9(x)+52=9(8)+52=72+52=124.\)
Since the angles ? and 9x+52 make up a line, they are supplementary. Therefore, we have
\(?=180-(9x+52)=180-124=\boxed{56}.\)
PLEASE HELP ME!! :(
If f(x) = 4x ^ 2 - 6 and g(x) = x ^ 2 - 4x - 8 , find (f - g)(x)
A. (f - g)(x) = 3x ^ 2 - 4x - 2
B. (f - g)(x) = 3x ^ 2 + 4x + 2
C. (f - g)(x) = 5x ^ 2 - 4x - 14
D. (f - g)(x) = - x ^ 2 - 14
Answers
Step-by-step explanation:
(f - g)(x)
= f(x) - g(x)
= (4x² - 6) - (x² - 4x - 8)
= 4x² - 6 - x² + 4x + 8
= 3x² + 4x + 2. (B)
Here is another problem
Answers
Answer:
Step-by-step explanation:
Answer:
all
Step-by-step explanation:
2x3=6 3x3=9 so 6:9
2x4=8 3x4=12 so 8:12
2x2=4 3x2=6 so 4:6
Lacey deposited $4,860 in a new credit union savings account on the first day of the quarter. The principal earns 4% interest compounded quarterly for 6 months.(a) the amount
Answers
Answer:
$4956.23 approx
Step-by-step explanation:
Given data
P= $4860
R= 4%
T= 6 months = 0.5 years
Applying the compound interest formula we have
A=P(1+r)^t
Substitute
A=4860(1+0.04)^0.5
A= 4860(1.04)^0.5
A=4860*1.0198
A=4956.228
Hence the balance will be $4956.23 approx
According to Hooke's Law, the force needed to stretch a spring varies directly to the amount the spring is stretched. If 50 pounds of force stretches a spring five inches, how much will the spring be stretched by a force of 180 pounds? inches
Answers
The length a spring stretches when subjected to the given load is required.
The spring is stretched by 18 inches.
Hooke's lawF = Force
k = Spring constant
x = Stretched length
\(F=50\ \text{lbf}\)
\(x=5\ \text{inch}\)
Hooke's law is given by
\(F=kx\\\Rightarrow 50=k5\\\Rightarrow k=\dfrac{50}{5}\\\Rightarrow k=10\ \text{lbf/inch}\)
\(F=180\ \text{lbf}\)
For the required spring
\(F=kx\\\Rightarrow x=\dfrac{F}{k}\\\Rightarrow x=\dfrac{180}{10}\\\Rightarrow x=18\ \text{inches}\)
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give answer to 1 d.p
Answers
Answer:
AB ≈ 5.6 cm
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos62° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{AB}{BC}\) = \(\frac{AB}{12}\) ( multiply both sides by 12 )
12 × cos62° = AB , then
AB ≈ 5.6 cm ( to 1 dec. place )
How do you know it is positive or negative in exponents.
Answers
Solve for x.
lesser x =
greater x =
Answers
Answer:
-1 = x 1 = x
Step-by-step explanation:
We want to factor this first
-4x^2 = -4
x^2=1
sqrt x^2 = sqrt 1
x = ± 1
x=-1 x=1
A plane travels at a speed of 160 mph in still air. Flying with a tailwind, the plane is clocked over a distance of 550 miles. Flying against a headwind, it takes 2 hourslonger to complete the return trip. What was the wind velocity? (Round your answer to the nearest tenth.)AnswerKeypad
Answers
ANSWER
The wind velocity is 43.2 miles
EXPLANATION
Given information
The total distance covered by the plane when flying with a tailwind is 550 miles
The total time = 2 hours
Let w represents the velocity of the wind
The speed with the wind = (160 + w)
The speed against the wind = (160 - w)
To find the wind velocity, follow the steps below
Step 1: Write the formula for writing distance
\(\text{ Speed = }\frac{distance\text{ }}{time}\)Step 2: Find the time for the plane to travel with the wind
\(\begin{gathered} \text{ speed = }\frac{\text{ distance}}{time} \\ cross\text{ multiply} \\ distance\text{ = speed }\times\text{ time} \\ time\text{ = }\frac{distance}{speed} \\ time\text{ = }\frac{550}{(160\text{ + w\rparen}} \\ Hence,\text{ the time required for the plane to travel with wind is }\frac{550}{(160+\text{ w\rparen}} \end{gathered}\)Step 3: Find the time for the plane to travel against the wind
\(\begin{gathered} \text{ speed = }\frac{distance}{time} \\ cross\text{ multiply} \\ distance\text{ = speed }\times time \\ time\text{ = }\frac{distance\text{ }}{speed} \\ time\text{ = }\frac{550}{(160-\text{ w\rparen}} \end{gathered}\)Recall, that the total time is time against - time with
\(Time\text{ = Time against - time with}\)Step 4:Substiute the value got in steps 2 and 3 into the formula in step 4
\(2\text{ = }\frac{550}{(160\text{ - w\rparen}}\text{ - }\frac{550}{(160+\text{ w\rparen}}\)Step 5: Simplify the above expression
\(\begin{gathered} The\text{ common denominator = \lparen160 - w\rparen \lparen160 + w\rparen} \\ 2\text{ = }\frac{(160\text{ + w \rparen}\times550\text{ - \lparen160 - w\rparen}\times550}{(160-\text{ w\rparen\lparen160 + w\rparen}} \\ open\text{ the parentheses} \\ 2\text{ = }\frac{88000\text{ + 550w - 88000+ 550w}}{25600\text{ + 160w - 160w - w}^2} \\ collect\text{ the like terms} \\ 2\text{ = }\frac{88000\text{ - 88000 + 550w - 150 w}}{25600\text{ - w}^2} \\ 2=\text{ }\frac{1100w}{25600\text{ - w}^2} \\ cross\text{ multiply} \\ 1100w\text{ = 2\lparen25600 - w}^2) \\ 1100w\text{= 51200 - 2w}^2 \\ 1100w\text{ - 51200 + 2w}^2 \\ 2w^2\text{ +1100w -51200} \\ \end{gathered}\)Step 6: Simplify the quadratic function using the general formula
\(\begin{gathered} 2w^2\text{ - 51200 +1100w} \\ \text{ Using, }\frac{-b\pm\sqrt{b^2\text{ - 4ac}}}{2a} \\ a\text{ = 2, b = 1100 c = -51200} \\ w\text{ = }\frac{-(1100)\pm\text{ }\sqrt{(1100^2\text{ - 4\lparen2 }\times\text{ -51200\rparen}}}{2\times2} \\ w\text{ = }\frac{-1100\pm\sqrt{1210000\text{ + 409600}}}{4} \\ w\text{ = }\frac{-1100\pm\sqrt{1619600}}{4} \\ w\text{ = }\frac{-1100\pm1272.635}{4} \\ \text{w = }\frac{-1100\text{ + 1272.635}}{4} \\ w\text{ = }\frac{172.635}{4} \\ w\text{ = 43.2 mile} \end{gathered}\)Hence, the wind velocity is 43.2 miles
Determine whether each function represents exponential growth or exponential decay. Move each function into the appropriate category
Answers
By analyzing the bases of the exponential equations, we can see that:
Exponential decay Exponential growth.
h(x) = 1.02*(0.06)^2 h(x) = 0.98*(3)^x
h(x) = 4*(0.74)^x h(x) = 9*(1.3)^x
Which functions are growths and which ones are decays?A general exponential function is written as:
f(x) = A*(b)^x
Where A is the initial value, b is the base, and x is the variable.
An exponential function is an exponential growth if b > 1.An exponential function is an exponential decay if 0 < b < 1The first one is:
h(x) = 0.98*(3)^x
The base is b = 3, so this is an exponential growth.
The second one is:
h(x) = 1.02*(0.06)^2
The base is b = 0.06, smaller than 1, then this is an exponential decay.
The third one is:
h(x) = 4*(0.74)^x
The base is b = 0.74, again this is smaller than 1, so we have an exponential decay.
The last one is:
h(x) = 9*(1.3)^x
The base is b = 1.3 > 1, then we have an exponential growth.
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Pls give simple working out
Answers
Answer:
x = 33
Step-by-step explanation:
∡ CBE = ∡DBA = 57°
The sum of the interior angles of a triangle results 180°
∡BDA = it´s a right angle = 90°
Then:
57° + 90° + x = 180°
147° + x = 180°
x = 180° - 147°
x = 33°
the total distance of a car moves varies directly with the time in hours.the car moves a total distance of 812 miles in 14 hours.what is the time in hours the car moves when the total distance is 1276 miles?
Answers
Answer:
J (22hrs)
Step-by-step explanation:
812 divided by 14= 58
1,276 divided by 58= 22 hrs
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Two stores sell CDs in packages, as shown in the table below.
CD Prices at Store A
Number of CDs in Package
1
12
20
45
Cost
$0.70
$8.40
?
$31.50
CD Prices at Store B
Number of CDs in Package
1
20
30
65
Cost
$0.60
?
$18.00
$39.00
If the rate at each store is constant, which statement correctly compares the cost of a package containing 20 CDs?
Answers
Hello.
In order to find this out, you have to multiply the amount of 1 CD and the amount of CDs.
In this case, we are finding out the amount of 20 CDs for each group.
Group A: Multiply 20 by 0.70; 20 x 0.70 = 14
The cost of 20 CDs for Group A is $14.00
Group B: Multiply 20 by 0.60; 20 x 0.60 = 12
The cost of 20 CDs for Group B is $12.00
Answer:
price of CDs at store A = 14 $
price of CDs at store B = 12 $
mark as brainlist answer
Given: AB = BC, AC is ∠ bisector of ∠BAD Prove: BC ∥ AD
Answers
Answer:
<BAC ≅ BCA by rule Base angle theorem
Step-by-step explanation:
What we know:
BAC = DAC
BC = BA
ΔBCA is an isosceles so ∠BCA = ∠DCA and ∠BAC
and we found that out by base angle theorem since
Base angle Theorem = Two base angles of a icosceles triangle are equal.
And since ΔBCA is an isoceles then ∠A and ∠C will be equal. And so we can prove BC is a parallel to AD
The proof that BC ∥ AD from the given statements is that;
BC ∥ AD because of the definition of alternate angles
We are given;
AB = BC
AC is ∠ bisector of ∠BAD
Since AC is the angle bisector of ∠BAD, it means that;
∠BAC = ∠DAC (definition of a bisected angle)
Now, since AB = BC, it means that ΔBCA is an isosceles triangle.
Thus; ∠BCA = ∠BAC (base angle theorem)
Now, since ∠BCA = ∠BAC, and ∠BAC = ∠DAC, we can say that;
∠BCA = ∠DAC
This means ∠BCA and ∠DAC are alternate angles. Thus, we can say that AC is the transversal line carrying the two equal angles.
Thus, we can say that BC is parallel to AD as they are the parallel lines cut by the transversal line AC.
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find a number if 0.7 of it is 3.43.
Answers
It shouldn’t be a trick question just fake 3.43 minus .7!
2y - 7 = 35
A
28
B
21
C
14
D
9
Answers
Answer:
Do u know the answer to
Step-by-step explanation:
Triangle ABC is a right triangle. The length of the legs are 3 in and 6 in, how long is the hypotenuse? (Round to the nearest tenth if necessary)
A) 3.3 in
B) 6.7 in
C) 7.9 in
D) 9.0 in
Answer:
21
Step-by-step explanation:
2y-7=35
2(21)-7 = 35
42-7= 35
35 =35
1. explain the The Butler–Volmer (BV)
2. Equation example of BV equation with values
3. a report on BV
Answers
1. The Butler-Volmer equation is an empirical equation used to describe electrochemical reaction kinetics at the electrode-electrolyte interface. 2. An example equation using the Butler-Volmer equation with values would depend on the specific electrochemical system and reaction being studied.
3. A report on the Butler-Volmer equation would typically involve an analysis of electrochemical reactions.
1. The Butler-Volmer equation is an empirical equation used to describe the kinetics of electrochemical reactions occurring at an electrode-electrolyte interface. It relates the rate of electrochemical reactions to the electrode potential and the concentrations of reactants in the electrolyte. The equation considers both the forward and backward reaction rates, taking into account the activation energy and the transfer of charge between the electrode and the electrolyte.
2. The general form of the Butler-Volmer equation is given as:
i = i₀[exp((αₐFη)/(RT)) - exp((-αᵦFη)/(RT))]
where:
i is the current density,
i₀ is the exchange current density,
αₐ and αᵦ are the anodic and cathodic charge transfer coefficients, respectively,
F is the Faraday's constant,
η is the overpotential (the difference between the electrode potential and the thermodynamic equilibrium potential),
R is the gas constant,
T is the temperature.
An example equation using the Butler-Volmer equation with values would depend on the specific electrochemical system and reaction being studied.
3. A report on the Butler-Volmer equation would typically involve an analysis of electrochemical reactions and their kinetics at the electrode-electrolyte interface. The report may include a theoretical background on the Butler-Volmer equation, its derivation, and its applications. It would also discuss experimental methods used to determine the parameters in the equation, such as the exchange current density and charge transfer coefficients. The report may present experimental data, discuss the limitations and assumptions of the equation, and compare the results with theoretical predictions.
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This is the question of 7 class opt math book. Write right answer.
Answers
Answer:
Step-by-step explanation:
x + 50 + 90 = 180
x + 140 = 180
x = 40 degrees
describe the sequence of transformations that could verify that the two triangles f and c are similar. give detail on each transformation.
Answers
The transformation that verify that the two triangles f and c are similar are
RotationTranslationDilationHow to map the transformation of F to CRotation: The first procedure is rotating triangle C with center art vertex (-9, 2) counterclockwise 90 degrees
Translation: In this case, the triangle is to the right 1 unit and 2 units up
Dilation: The dilation factor here is 2. Using the vertex of of the point which is (-8, 0) as the center, dilate with a scale factor of two
The transformations described moves triangle F to triangle C
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I will report you for any not serious answers, and the points will be taken away from you.
I have the answer of 8 for x, but does 3 WORK for x?
Because my answer choices consists of 24, but not 8.
My big question is "is 3 a valid solution"
Answers
Answer:
i don't think 3 works for x because the only solution for x was 8
Step-by-step explanation:
Which rate describes a unit price. $1.00 for 2 lemons. $3.00 for every pound. $4.00 for 3 slices of pizza. $6.00 for every 6 bottles.
Answers
Answer:
I believe it would be $3 per pound.
Let me know if I'm incorrect!
Answer:
It is C
Step-by-step explanation:
i can verify because i took the test and got 100
Consider a system whose wave function is given by ψ(θ,φ)=
2
1
Y
00
(θ,φ)+
3
1
Y
11
(θ,φ)+
2
1
Y
10
(θ,φ)+
6
1
Y
14
(θ,φ). Find the probability associafed with a measurement that gives 1 h for the z-component of the angular momentum. 2. 0.9 b. 0.5 c 0.8 d. 0.4 4. 05
Answers
The probability associated with measuring +1ℏ for the z-component of angular momentum is 9.
To find the probability associated with a measurement that gives +1ℏ for the z-component of the angular momentum, we need to calculate the square of the coefficient of the corresponding spherical harmonic in the wave function.
The wave function is given by:
ψ(θ, φ) = 2Y₀₀(θ, φ) + 3Y₁₁(θ, φ) + 2Y₁₀(θ, φ) + 6Y₁₄(θ, φ)
The coefficient for the Y₁₁ term is 3, so the probability associated with measuring +1ℏ for the z-component of angular momentum is the square of this coefficient: |3|² = 9.
Therefore, the probability is 9.
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14. Describe the typical quiz scores of the students. Explain your choice of measure.
Answers
To describe the typical quiz scores of the students, a common measure used is the mean, or average, score. The mean is calculated by summing up all the scores and dividing by the total number of scores.
Given its simplicity and simplicity in interpretation, the mean was chosen as a proxy for normal quiz scores. It offers a solitary figure that encapsulates the scores' median. We can figure out the pupils' overall performance on the quiz scores by computing the mean.
It's crucial to keep in mind, though, that outliers or extremely high scores dividing might have an impact on the mean. The mean may not be an accurate representation of the normal results of the majority of students if there are a few students who severely underperform or do very well on the quizzes.
To get a more thorough picture of the distribution of quiz results in such circumstances, it might be beneficial to take into account additional metrics like the median or mode.
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What does it mean to have 2 equal roots?
Answers
Therefore , it means if an equation have 2 roots , it means it is a quadratic function .
What is square root ?A number's root is that factor of the number that, when multiplied by itself, yields the original number. Specifically, squares and square roots are exponents. Think of the number nine. This can be expressed as or as 3 x 3.
Here,
If an equation have 2 roots , it means it is a quadratic function
If D=0, a quadratic function has two roots that are equal.
D (discriminant) = 0
=>b24ac=0 is required for a polynomial function to have equal roots.
Therefore , it means if an equation have 2 roots , it means it is a quadratic function .
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True or false: Data analytics allows auditors to vastly expand sampling beyond current traditional sample sizes, but does not allow the ability to test the full population of transactions.
Answers
The given statement " Data analytics allows auditors to vastly expand sampling beyond current traditional sample sizes, but does not allow the ability to test the full population of transactions" is False because Data analytics allows auditors to provide the ability to test the full population of transactions.
Data analytics involves the use of advanced techniques and tools to analyze large volumes of data quickly and efficiently. It allows auditors to examine extensive datasets and identify patterns, anomalies, and trends that may indicate potential risks or issues. By analyzing a larger sample size, auditors can gain more comprehensive insights into the population being tested and make more informed conclusions.
However, even with data analytics, it is generally not feasible or necessary to test the full population of transactions. The sheer size and complexity of modern datasets make it impractical to examine every single transaction. Instead, auditors use statistical sampling techniques to select a representative sample from the population and then apply data analytics to analyze that sample.
While data analytics provides auditors with powerful tools to enhance the effectiveness and efficiency of their work, it does not eliminate the need for sampling. Sampling remains an essential part of the audit process to draw conclusions about the entire population based on the characteristics observed in the selected sample.
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Listed below is a series of experiments and associated random variables. In each case, identify the values that the random variable can assume and state whethe is discrete or continuous. Experiment Random Variable (x) Values Continuo a. Take a 15-question examination Select your answer - ✓ - Select your answ Number of questions answered correctly Number of cars arriving at tollbooth - Select your answer - V - Select your answ b. Observe cars arriving at a tollbooth for 1 hour c. Audit 50 tax returns Number of returns containing errors - Select your answer - - Select your answ Select your answer - - Select your answ d. Observe an employee's work Number of nonproductive hours in an nine-hour workday e. Weigh a shipment of goods Number of pounds Select your answer - - Select your answ of experiments and associated random variables. In each case, identify the values that the random variable can assume and state whether the random variable S. xperiment Random Variable (x) Values Continuous or Discrete examination - Select your answer - - Select your answer - Number of questions answered correctly Number of cars arriving at tollbooth g at a tollbooth for 1 hour - Select your answer - ✓ - Select your answer - Select your answer - Number of returns containing errors - Select your answer - ✓ - Select your answer - - Select your answer - V ee's work Number of nonproductive hours in an nine-hour workday f goods Number of pounds - Select your answer - - Select your answer - V
Answers
This is because the number of pounds can take on an infinite number of values within a range.
The following table shows a series of experiments and associated random variables:ExperimentRandom Variable (x)Values
Continuous or Discrete
a. Take a 15-question examinationNumber of questions answered correctlyDiscreteb. Observe cars arriving at a tollbooth for 1 hourNumber of cars arriving at tollboothDiscretec. Audit 50 tax returnsNumber of returns containing errorsDiscreted. Observe an employee's workNumber of nonproductive hours in a nine-hour workdayDiscretee. Weigh a shipment of goodsNumber of poundsContinuous
The random variable in experiment a is discrete. This is because the number of questions answered correctly can only take on a finite number of values.The random variable in experiment b is also discrete. This is because the number of cars arriving at the tollbooth can only take on a finite number of values.The random variable in experiment c is also discrete. This is because the number of returns containing errors can only take on a finite number of values.The random variable in experiment d is discrete. This is because the number of nonproductive hours in a nine-hour workday can only take on a finite number of values.The random variable in experiment e is continuous.
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Maria orders t-shirts for her volleyball camp. Adult-sized T-Shirts cost $6.25 each and youth-sized T-Shirts cost $4.50. Maria has $550 to purchase both adult-sized and youth-sized T-Shirts. If she purchases 45 youth-sized T-Shirts, determine algebraically the maximum number of adult-sized T-Shirts she can purchase.
Answers
Answer:
55
Step-by-step explanation:
45 * 4.50 = 202.5
550 - 202.5 = 347.5
347.5/6.25 = 55.6 (55 full t shirts)
the scale on a map is 1:10 000
a) two towns are 17km apart
how far apart would the be on the map?
give your answers in centimeters.
b) the viewpoint and the pier are 7.1cm apart on the map.
how far apart would they be in real life?
give your answers in kilometers.
Answers
PLEASE HELP ASAP!!
The equation
6x + 4 = 5x + 12 + x - 8
is true for all real numbers.
Substitute a few real numbers for x to see that this is so and then try solving the equation.
Describe what happens.
Choose the correct answer below.
A.
The left side of the equation is the reciprocal of the right side of the equation.
B.
The left side of the equation is never equal to the right side of the equation.
C.
The left side of the equation is always equal to the right side of the equation.
D.
The left side of the equation is the additive inverse of the right side of the equation.
Answers
7) Determine the equation of the line in the form y=mx+B that goes through the two points (5,10) and (9,20).
Answers
First, let's calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (5, 10) and (9, 20), we have:
m = (20 - 10) / (9 - 5) = 10 / 4 = 2.5
Now that we have the slope (m = 2.5), we can substitute it into the equation y = mx + b and use one of the given points to solve for the y-intercept (b).
Let's use the point (5, 10):
10 = 2.5(5) + b
10 = 12.5 + b
b = 10 - 12.5
b = -2.5
Therefore, the equation of the line that passes through the points (5, 10) and (9, 20) is:
y = 2.5x - 2.5