Question 1

A company's cost function to produce x units of one product and y units of a second product is given by  .
The minimum cost occurs when x = _____ and y = _____.

Accepted Answer

The answer of A company's cost function to produce x...

Question 2

A company manufactures x units of one item and y units of another. The total cost, C, in dollars of producing these two items is given by the function  .
Use Lagrange multipliers to find the minimum cost subject to the constraint that 100 items (total) must be produced. The minimum cost occurs when x = _____ and y = _____. Round your answers to the nearest whole number.

Accepted Answer

The answer of A company manufactures x units of one...

Question 3

The number, N, of children that can be enrolled in a private school is a function of the number of certified teachers, T, and the number of aides, A, available, according to the formula  . Teachers average an annual salary of $38,000 and aides average an annual salary of $20,000. The annual budget for salaries is B = $800,000. If we want to maximize enrollment, which of the following is true?
A)The objective function is  , and the constraint is
 .
B)The objective function is  , and the constraint is
 .
C)The objective function is  , and the constraint is
 .
D)The objective function is  , and the constraint is
 .

Accepted Answer

The answer of The number, N, of children that can...

Question 4

If , find f_x . A)2xy + x² B)2xy + y² + 3 C) D)

Accepted Answer

The answer of If , find f_x ...

Question 5

The monthly car payment for a new car is a function of three variables, , where r is the annual interest rate, A is the amount borrowed in dollars, and t is time in months before the car is paid off. Would you expect f_A to be increasing or decreasing?

Accepted Answer

The answer of The monthly car payment for a new...

Question 6

If  , find  r  t.
A) 
B) 
C) 
D)

Accepted Answer

The answer of If  , find  r ...

Question 7

The number, N, of children that can be enrolled in a private school is a function of the number of certified teachers, T, and the number of aides, A, available, according to the formula  .
Teachers average an annual salary of $34,000 and aides average an annual salary of $24,000. The annual budget for salaries is B = $760,000. Using Lagrange multipliers to maximize enrollment, we find that T = _____, A = _____, and  = _____. Round T and A to the nearest whole number; round  to 5 decimal places.

Accepted Answer

The answer of The number, N, of children that can...

Question 8

Which of the following contour diagrams is more likely to show the population density of a region of a small town where the center of the diagram is the town center?
I.  II.

Accepted Answer

The answer of Which of the following contour diagrams is...

Question 9

If , find r^2. A)5r² B)5t² C)-5r² D)-5t²

Accepted Answer

The answer of If , find r^2. A)5r² ^...

Question 10

Given the following table of values for , estimate f_y (10,0.2). Use the next higher point to make your estimate.

Accepted Answer

The answer of Given the following table of values for...

Question 11

If , does f_yy = ?

Accepted Answer

The answer of If , does f_yy ...

Question 12

The critical point of  occurs at x = _____, y = _____, and is a local ________ (maximum / minimum / neither).

Accepted Answer

The answer of The critical point of  occurs at...

Question 13

A company manufactures x units of one item and y units of another. The total cost, C, in dollars of producing these two items is given by the function  .
Use Lagrange multipliers to find the minimum cost subject to the constraint that 100 items (total) must be produced. What is the value of  to one decimal place?

Accepted Answer

The answer of A company manufactures x units of one...

Question 14

A manufacturer sells two products. The first sells for $7 and the second sells for $5. The manufacturer's costs are given by the equation  ,
where  and  are the respective quantities produced of each product. Let  represent the profit at a production level of  and  units. Find the value of  .

Accepted Answer

The answer of A manufacturer sells two products. The first...

Quiz 8: Functions of Several Variables

A company's cost function to produce x units of one product and y units of a second product is given by . The minimum cost occurs when x = _ and y = _.

If , find f_x .

The monthly car payment for a new car is a function of three variables, , where r is the annual interest rate, A is the amount borrowed in dollars, and t is time in months before the car is paid off. Would you expect f_A to be increasing or decreasing?

If , find r t.

Which of the following contour diagrams is more likely to show the population density of a region of a small town where the center of the diagram is the town center? I. II.

If , find r^2.

Given the following table of values for , estimate f_y (10,0.2). Use the next higher point to make your estimate.

If , does f_yy = ?

The critical point of occurs at x = ___, y = _, and is a local ______ (maximum / minimum / neither).

A manufacturer sells two products. The first sells for $7 and the second sells for $5. The manufacturer's costs are given by the equation , where and are the respective quantities produced of each product. Let represent the profit at a production level of and units. Find the value of .

Quiz 8: Functions of Several Variables

A company's cost function to produce x units of one product and y units of a second product is given by . The minimum cost occurs when x = _____ and y = _____.

If , find fx .

The monthly car payment for a new car is a function of three variables, , where r is the annual interest rate, A is the amount borrowed in dollars, and t is time in months before the car is paid off. Would you expect fA to be increasing or decreasing?

If , find r t.

Which of the following contour diagrams is more likely to show the population density of a region of a small town where the center of the diagram is the town center? I. II.

If , find r2.

Given the following table of values for , estimate fy (10,0.2). Use the next higher point to make your estimate.

If , does fyy = ?

The critical point of occurs at x = _____, y = _____, and is a local ________ (maximum / minimum / neither).

A manufacturer sells two products. The first sells for $7 and the second sells for $5. The manufacturer's costs are given by the equation , where and are the respective quantities produced of each product. Let represent the profit at a production level of and units. Find the value of .

A company's cost function to produce x units of one product and y units of a second product is given by . The minimum cost occurs when x = _ and y = _.

If , find f_x .

The monthly car payment for a new car is a function of three variables, , where r is the annual interest rate, A is the amount borrowed in dollars, and t is time in months before the car is paid off. Would you expect f_A to be increasing or decreasing?

If , find r^2.

Given the following table of values for , estimate f_y (10,0.2). Use the next higher point to make your estimate.

If , does f_yy = ?

The critical point of occurs at x = ___, y = _, and is a local ______ (maximum / minimum / neither).