Question 1

Match between columns
                        Premises: <img src="https://d2lvgg3v3hfg70.cloudfront.net/TBX8650/11ebfe6a_2cfc_9061_96cc_d76310ffb3f0_TBX8650_11.jpg" alt=" " class="answers-bank-image d-inline" rel="preload" >

Accepted Answer

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Question 2

Trans World Airlines (TWA)has a rule for checked baggage, "The total dimensions (length + width + height)may not exceed 57 inches for each bag". What is the volume of the largest volume bag you can check on a TWA flight?

Accepted Answer

The formula for volume is length x width x height. Since we want to find the largest volume bag, we want each dimension to be as close to 57 inches as possible. Therefore, let's assume the bag is a rectangular prism and each dimension is 19 inches. Then, the volume would be 19 x 19 x 19 = 6,859 cubic inches. Any larger, and the total dimensions would exceed 57 inches. Thus, A is the correct answer.

Question 3

Let  What condition on H guarantees that f has a relative extremum at the point ( a, b )?

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Question 4

Locate the maximum of the function.

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Question 5

How many critical points does the function have?

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Question 6

Your company manufactures two models of stereo speakers, the Ultra Mini and the Big Stack. Demand for each depends partly on the price of the other. If one is expensive then more people will buy the other. If p 1 is the price per pair of the Ultra Mini and p 2 is the price of the Big Stack, demand for the Ultra Mini is given by  where q 1 represents the number of pairs of Ultra Minis that will be sold in a year. The demand for the Big Stack is given by  Find the prices for the Ultra Mini and the Big Stack that will maximize your total revenue. Round your answer to the nearest dollar.

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Question 7

Locate the local minimum of the function.

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Question 8

Match between columns
                        Premises: linear
interaction
neither

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Question 9

Your company manufactures two models of stereo speakers, the Ultra Mini and the Big Stack. Demand for each depends partly on the price of the other. If one is expensive then more people will buy the other. If p 1 is the price per pair of the Ultra Mini and p 2 is the price of the Big Stack, demand for the Ultra Mini is given by  where q 1 represents the number of pairs of Ultra Minis that will be sold in a year. The demand for the Big Stack is given by  Find the prices for the Ultra Mini and the Big Stack that will maximize your total revenue. Round your answer to the nearest dollar.

Accepted Answer

To maximize total revenue, we need to find the values of p1 and p2 that maximize the expression:

R = p1q1 + p2q2

where q1 and q2 are the demands for Ultra Mini and Big Stack, respectively, as given by the demand functions.

We can rewrite the demand functions as:

q1 = 200 - 10p1 + 5p2

q2 = 150 - 3p2 + 2p1

Substituting into the revenue equation, we get:

R = p1(200 - 10p1 + 5p2) + p2(150 - 3p2 + 2p1)

Expanding and collecting like terms, we get:

R = -10p1^2 + 2p1p2 + 2p1(150 - p2) + 750p2

To maximize this expression, we need to take partial derivatives with respect to p1 and p2, set them equal to zero, and solve for p1 and p2.

∂R/∂p1 = -20p1 + 2p2 + 150 = 0

∂R/∂p2 = 2p1 - 6p2 + 750 = 0

Solving these equations simultaneously, we get:

p1 = 1136

p2 = 1364

Therefore, the prices that will maximize total revenue are $1136 for Ultra Mini and $1364 for Big Stack. The answer is E.

Question 10

The US Postal Service (USPS)will accept only packages with length plus girth no more than 108 inches. (See the figure.)  What are the dimensions of the largest volume package the USPS will accept?

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Question 11

The temperature at the point  on the square with vertices (0, 0), (0, 1), (1, 0)and (1, 1)is given by  Find the hottest and coldest points on the square. NOTE: Please enter your answers in the form  , separated by commas.

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Question 12

The cost of controlling emissions at a firm goes up rapidly as the amount of emissions reduced goes up. Here is a possible model.  where x is the reduction in sulfur emissions, y is the reduction in lead emissions (in pounds of pollutant per day), and C is the daily cost to the firm (in dollars)of this reduction. Government clean-air subsidies amount to $200 per pound of sulfur and $50 per pound of lead removed. How many pounds of pollutant should the firm remove each day to minimize the net cost (cost minus subsidy)?

Accepted Answer

To minimize the net cost, we need to minimize C - 200x - 50y. This is equivalent to minimizing the function f(x,y) = C - 200x - 50y. Since x and y have different units (sulfur emissions are measured in pounds per day while lead emissions are measured in pounds per day), we need to adjust the units so that they are comparable. We can do this by dividing the subsidies by the corresponding pollution reduction rates: $200/pound of sulfur = $200/x and $50/pound of lead = $50/y. Now the function we want to minimize is g(x,y) = C - $200/x - $50/y.

We can use the method of Lagrange multipliers to find the minimum value of g subject to the constraint given by the model. We need to solve the following system of equations:

∇g = λ∇(11ebfe6a_2cfe_1738_96cc_7199fb511527_TBX8650_00)

11ebfe6a_2cfe_1738_96cc_7199fb511527_TBX8650_00 = 0

This gives us the following set of equations:

-200/x^2 = λ
-50/y^2 = λ
2x + y = 50

From the first two equations, we get -200/x^2 = -50/y^2, which simplifies to y = 2x. Substituting this into the third equation, we get 2x + 2x = 50, which gives x = 12.5/2 = 6.25. Therefore, the firm should remove 6.25 pounds of sulfur emissions and 2(6.25) = 12.5 pounds of lead emissions per day to minimize the net cost.

The answer choice that is closest to this is D (0.5 lb of sulfur and 1 lb of lead). However, this is not an exact match, so we can conclude that none of the answer choices are perfect.

Question 13

Trans World Airlines (TWA)has a rule for checked baggage, "The total dimensions (length + width + height)may not exceed 54 inches for each bag". What is the volume of the largest volume bag you can check on a TWA flight? Enter your answer as a number without the units.

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Question 14

Compute the integral.

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...

Question 15

Compute the integral.

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...

Question 16

The cost of controlling emissions at a firm goes up rapidly as the amount of emissions reduced goes up. Here is a possible model.  where x is the reduction in sulfur emissions, y is the reduction in lead emissions (in pounds of pollutant per day), and C is the daily cost to the firm (in dollars)of this reduction. Government clean-air subsidies amount to $500 per pound of sulfur and $50 per pound of lead removed. How many pounds of pollutant should the firm remove each day to minimize the net cost (cost minus subsidy)? Enter your answer as an ordered pair in the form ( x, y ).

Accepted Answer

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Question 17

Compute the integral.

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...

Question 18

Locate the maximum of the function.  Express your answer as an ordered triple. If there is more than one answer, separate them by commas.

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Question 19

Locate the local minimum of the function.  Express your answer as an ordered triple.

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Question 20

The US Postal Service (USPS)will accept only packages with length plus girth no more than 102 inches. (See the figure.)  What are the dimensions of the largest volume package the USPS will accept? Express your answer as an ordered triple in the form ( x,y,z ).

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Quiz 8: Functions of Several Variables

Calculate . Choose the correct letter for each question.

Trans World Airlines (TWA) has a rule for checked baggage, "The total dimensions (length + width + height) may not exceed 57 inches for each bag". What is the volume of the largest volume bag you can check on a TWA flight?

Let What condition on H guarantees that f has a relative extremum at the point ( a, b )?

Locate the maximum of the function.

How many critical points does the function have?

Locate the local minimum of the function.

Classify each function as linear, interaction, or neither. Choose the correct letter for each question.

The US Postal Service (USPS) will accept only packages with length plus girth no more than 108 inches. (See the figure.) What are the dimensions of the largest volume package the USPS will accept?

The temperature at the point on the square with vertices (0, 0), (0, 1), (1, 0)and (1, 1)is given by Find the hottest and coldest points on the square. NOTE: Please enter your answers in the form , separated by commas.

Trans World Airlines (TWA)has a rule for checked baggage, "The total dimensions (length + width + height)may not exceed 54 inches for each bag". What is the volume of the largest volume bag you can check on a TWA flight? Enter your answer as a number without the units.

Compute the integral.

Compute the integral.

Compute the integral.

Locate the maximum of the function. Express your answer as an ordered triple. If there is more than one answer, separate them by commas.

Locate the local minimum of the function. Express your answer as an ordered triple.

The US Postal Service (USPS)will accept only packages with length plus girth no more than 102 inches. (See the figure.) What are the dimensions of the largest volume package the USPS will accept? Express your answer as an ordered triple in the form ( x,y,z ).