Question 1

Test for relative maximum and minimum. ​  ​
A) relative minimum at 
B) relative maximum at 
C) relative minimum at 
D) relative maximum at 
E) relative minimum at

Accepted Answer

The answer of Test for relative maximum and minimum. ​...

Question 2

Suppose that x units of one input and y units of a second input result in  units of a product. What is the maximum production? ​
A) 1,675
B) ​3,081
C) ​1,152
D) ​1,027
E) ​1,425

Accepted Answer

The answer of Suppose that x units of one input...

Question 3

Use the points given in the table to write the equation of the line that is the best fit for the points. Round numerical values in your answer to two decimal places. ​

A) 
B) ​ 
C) ​ 
D) ​ 
E) ​

Accepted Answer

The answer of Use the points given in the table...

Question 4

A new food is designed to add weight to mature beef cattle. The weight in pounds is given by  , where x is the number of units of the first ingredient and y is the number of units of the second ingredient. How many units of each ingredient will maximize the weight? ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of A new food is designed to add...

Question 5

Test for relative maximum and minimum. ​  ​
A) relative maxima when x = 7, y = -8 and x = 7, y = 8; relative minima when x = -7, y = 8 and x = -7, y = -8
B) relative maximum when x = 7, y = -8; relative minimum when x = -7, y = 8
C) saddle point when x = -7, y = -8; relative minima when x = 0, y = 0 and x = -7, y = -8
D) saddle points when x = 7, y = -8 and x = -7, y = 8; relative maximum when x = -7, y = -8; relative minimum when x = 7, y = 8
E) saddle points when x = 7, y = 8 and x = -7, y = -8; relative maxima when x = 7, y = -8 and x = -7, y = 8

Accepted Answer

The answer of Test for relative maximum and minimum. ​...

Question 6

Find the values for each of the dimensions of a closed-top box of length x, width y, and height z (in inches) if the volume equals 32,768 cubic inches and the box requires the least amount of material to make. ​
A) x = 46 inches, y = 46 inches, z = 46 inches
B) x = 32 inches, y = 32 inches, z = 32 inches
C) x = 41 inches, y = 41 inches, z = 41 inches
D) x = 45 inches, y = 45 inches, z = 45 inches
E) x = 34 inches, y = 34 inches, z = 34 inches

Accepted Answer

The box that requires the least amount of material for a given volume is a cube. The volume of a cube is given by $V = s^3$, where $s$ is the side length. To find the side length for a volume of 32,768 cubic inches, we solve $32,768 = s^3$, which gives $s = 32$ inches. Therefore, the dimensions that require the least material are $x = y = z = 32$ inches.

Question 7

The following table gives the actual or projected population in millions for a certain city for selected years from 2000 to 2050. Use linear regression to find the linear equation that is the best fit for the data, with x equal to the number of years past 2000. ​

A) 
B) ​ 
C) ​ 
D) ​ 
E) ​

Accepted Answer

The answer of The following table gives the actual or...

Question 8

The following table shows the median age of automobiles and trucks on the road for a certain country. Use linear regression to find the linear equation that is the best fit for the data, with x equal to the number of years past 1980. ​

A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of The following table shows the median age...

Question 9

Test for relative maximum and minimum. ​  ​
A) relative minimum at  and saddle point at 
B) relative maximum at  and saddle point at 
C) relative minimum at 
D) relative maximum at 
E) saddle points at  and

Accepted Answer

The answer of Test for relative maximum and minimum. ​...

Question 10

Test for relative maximum and minimum. ​  ​
A) relative maximum at 
B) relative maximum at 
C) relative minimum at 
D) relative minimum at 
E) relative minimum at

Accepted Answer

This question cannot be answered without a graphical representation of the function.

Question 11

Suppose that  tons is the production function for a product with x units of one input and y units of a second input. Find the values of x and y that will maximize production. ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Suppose that  tons is the production...

Question 12

Find the values for each of the dimensions of an open-top box of length x, width y, and height  (in inches) such that the box requires the least amount of material to make. ​
A) length = 8 inches
Width = 8 inches
Height = 4 inches
B) length = 4 inches
Width = 8 inches
Height = 8 inches
C) length = 8 inches
Width = 4 inches
Height = 8 inches
D) length = 4 inches
Width = 4 inches
Height = 16 inches
E) length = 16 inches
Width = 4 inches
Height = 4 inches

Accepted Answer

The answer of Find the values for each of the...

Question 13

A company manufactures two products, A and B. If x is the number of thousands of units of A and y is the number of thousands of units of B, then the cost and revenue in thousands of dollars are ​  ​
Find the number of each type of product that should be manufactured to maximize profit.
​
A) 3,000 units of product A
48,000 units of product B
B) 6,000 units of product A
24,000 units of product B
C) 12,000 units of product A
12,000 units of product B
D) 3,000 units of product A
12,000 units of product B
E) 12,000 units of product A
48,000 units of product B

Accepted Answer

The answer of A company manufactures two products, A and...

Question 14

Test for relative maximum and minimum. ​  ​
A) saddle point at 
B) saddle point at 
C) saddle point at 
D) relative minimum at 
E) relative minimum at

Accepted Answer

The answer of Test for relative maximum and minimum. ​...

Question 15

Suppose that a manufacturer produces two brands of a product, brand 1 and brand 2. Suppose the demand for brand 1 is thousand units and the demand for brand 2 is thousand units, where p₁ and p₂ prices in dollars. If the joint cost function is , in thousands of dollars, how many of each brand should be produced to maximize profit? A) 74 units of brand 1 82 units of brand 2 B) 9 units of brand 1 52 units of brand 2 C) 74 units of brand 1 52 units of brand 2 D) 14 units of brand 1 38 units of brand 2 E) 27 units of brand 1 77 units of brand 2

Accepted Answer

The answer of Suppose that a manufacturer produces two brands...

Question 16

Test for relative maximum and minimum. ​  ​
A) relative maximum at 
B) saddle point at 
C) relative maximum at 
D) relative minimum at 
E) saddle point at

Accepted Answer

The answer of Test for relative maximum and minimum. ​...

Question 17

Test for relative maximum and minimum. ​  ​
A) relative minimum at 
B) relative maximum at 
C) saddle point at 
D) relative maximum at 
E) relative minimum at

Accepted Answer

The answer of Test for relative maximum and minimum. ​...

Question 18

Suppose that the data in the table below shows the average earnings of year-round full-time workers by gender for several different levels of educational attainment. Find and interpret the slope of the linear regression line. Round the slope to three decimal places. ​

A) The slope is 0.910. The average annual earnings of females is decreasing at a rate of $0.910 per dollar increase in the annual of males.
B) The slope is 0.807. The average annual earnings of females is decreasing at a rate of $0.807 per dollar decrease in the average annual earnings of males.
C) The slope is 0.759. The average annual earnings of females is decreasing at a rate of $0.759 per dollar decrease in the average annual earnings of males.
D) The slope is 0.900. The average annual earnings of females is increasing at a rate of $0.900 per dollar increase in the average annual earnings of males.
E) The slope is 0.749. The average annual earnings of females is increasing at a rate of $0.749 per dollar increase in the average annual earnings of males.

Accepted Answer

The slope is 0.900. This means that for each dollar increase in the average annual earnings of males, the average annual earnings of females are increasing at a rate of $0.900.

Question 19

Test  for relative maximum and minimum. ​
A) The point  is a saddle point.
A relative maximum occurs at  .
B) The point  is a saddle point.
A relative maximum occurs at  .
C) The point  is a saddle point.
A relative maximum occurs at  .
D) The point  is a saddle point.
A relative minimum occurs at  .
E) The point  is a saddle point.
A relative minimum occurs at  .

Accepted Answer

The answer of Test  for relative maximum and minimum....

Question 20

Suppose that the profit from the sale of Kandy and Kreams is given by  dollars, where x is the number of pounds of Kandy and y is the number of pounds of Kreams. How many pounds of Kandy and Kreams must be sold to maximize profit? What is the maximum profit? Round your pounds answers to the nearest whole number. Round your max profit answer to the nearest cent. ​
A) 40 pounds of Kandy, 200 pounds of Kreams, max profit of $661.00
B) 6 pounds of Kandy, 15 pounds of Kreams, max profit of $477.45
C) 12 pounds of Kandy, 30 pounds of Kreams, max profit of $865.80
D) 20 pounds of Kandy, 100 pounds of Kreams, max profit of $1,620.00
E) 60 pounds of Kandy, 300 pounds of Kreams, max profit of $315.34

Accepted Answer

To maximize profit, we need to find the critical point of the given function. Taking partial derivatives and setting them equal to zero, we get:
11 - 0.02x - 0.05y = 0
and
11 - 0.05x - 0.02y = 0
Solving these equations simultaneously, we get x = 20 and y = 100. Therefore, 20 pounds of Kandy and 100 pounds of Kreams must be sold to maximize profit. Substituting these values back into the given function, we get maximum profit of $1,620.00.

Quiz 14: Functions of Two or More Variables

Test for relative maximum and minimum.

Suppose that x units of one input and y units of a second input result in units of a product. What is the maximum production?

Use the points given in the table to write the equation of the line that is the best fit for the points. Round numerical values in your answer to two decimal places.

A new food is designed to add weight to mature beef cattle. The weight in pounds is given by , where x is the number of units of the first ingredient and y is the number of units of the second ingredient. How many units of each ingredient will maximize the weight?

Test for relative maximum and minimum.

Find the values for each of the dimensions of a closed-top box of length x, width y, and height z (in inches) if the volume equals 32,768 cubic inches and the box requires the least amount of material to make.

The following table gives the actual or projected population in millions for a certain city for selected years from 2000 to 2050. Use linear regression to find the linear equation that is the best fit for the data, with x equal to the number of years past 2000.

The following table shows the median age of automobiles and trucks on the road for a certain country. Use linear regression to find the linear equation that is the best fit for the data, with x equal to the number of years past 1980.

Test for relative maximum and minimum.

Test for relative maximum and minimum.

Suppose that tons is the production function for a product with x units of one input and y units of a second input. Find the values of x and y that will maximize production.

Find the values for each of the dimensions of an open-top box of length x, width y, and height (in inches) such that the box requires the least amount of material to make.

A company manufactures two products, A and B. If x is the number of thousands of units of A and y is the number of thousands of units of B, then the cost and revenue in thousands of dollars are Find the number of each type of product that should be manufactured to maximize profit.

Test for relative maximum and minimum.

Test for relative maximum and minimum.

Test for relative maximum and minimum.

Suppose that the data in the table below shows the average earnings of year-round full-time workers by gender for several different levels of educational attainment. Find and interpret the slope of the linear regression line. Round the slope to three decimal places.

Test for relative maximum and minimum.

Quiz 14: Functions of Two or More Variables

Test for relative maximum and minimum. ​ ​

Suppose that x units of one input and y units of a second input result in units of a product. What is the maximum production? ​

Use the points given in the table to write the equation of the line that is the best fit for the points. Round numerical values in your answer to two decimal places. ​

A new food is designed to add weight to mature beef cattle. The weight in pounds is given by , where x is the number of units of the first ingredient and y is the number of units of the second ingredient. How many units of each ingredient will maximize the weight? ​

Test for relative maximum and minimum. ​ ​

Find the values for each of the dimensions of a closed-top box of length x, width y, and height z (in inches) if the volume equals 32,768 cubic inches and the box requires the least amount of material to make. ​

The following table gives the actual or projected population in millions for a certain city for selected years from 2000 to 2050. Use linear regression to find the linear equation that is the best fit for the data, with x equal to the number of years past 2000. ​

The following table shows the median age of automobiles and trucks on the road for a certain country. Use linear regression to find the linear equation that is the best fit for the data, with x equal to the number of years past 1980. ​

Test for relative maximum and minimum. ​ ​

Test for relative maximum and minimum. ​ ​

Suppose that tons is the production function for a product with x units of one input and y units of a second input. Find the values of x and y that will maximize production. ​

Find the values for each of the dimensions of an open-top box of length x, width y, and height (in inches) such that the box requires the least amount of material to make. ​

A company manufactures two products, A and B. If x is the number of thousands of units of A and y is the number of thousands of units of B, then the cost and revenue in thousands of dollars are ​ ​ Find the number of each type of product that should be manufactured to maximize profit. ​

Test for relative maximum and minimum. ​ ​

Test for relative maximum and minimum. ​ ​

Test for relative maximum and minimum. ​ ​

Suppose that the data in the table below shows the average earnings of year-round full-time workers by gender for several different levels of educational attainment. Find and interpret the slope of the linear regression line. Round the slope to three decimal places. ​

Test for relative maximum and minimum. ​

Test for relative maximum and minimum.

Suppose that x units of one input and y units of a second input result in units of a product. What is the maximum production?

Use the points given in the table to write the equation of the line that is the best fit for the points. Round numerical values in your answer to two decimal places.

A new food is designed to add weight to mature beef cattle. The weight in pounds is given by , where x is the number of units of the first ingredient and y is the number of units of the second ingredient. How many units of each ingredient will maximize the weight?

Test for relative maximum and minimum.

Find the values for each of the dimensions of a closed-top box of length x, width y, and height z (in inches) if the volume equals 32,768 cubic inches and the box requires the least amount of material to make.

The following table gives the actual or projected population in millions for a certain city for selected years from 2000 to 2050. Use linear regression to find the linear equation that is the best fit for the data, with x equal to the number of years past 2000.

The following table shows the median age of automobiles and trucks on the road for a certain country. Use linear regression to find the linear equation that is the best fit for the data, with x equal to the number of years past 1980.

Test for relative maximum and minimum.

Test for relative maximum and minimum.

Suppose that tons is the production function for a product with x units of one input and y units of a second input. Find the values of x and y that will maximize production.

Find the values for each of the dimensions of an open-top box of length x, width y, and height (in inches) such that the box requires the least amount of material to make.

A company manufactures two products, A and B. If x is the number of thousands of units of A and y is the number of thousands of units of B, then the cost and revenue in thousands of dollars are Find the number of each type of product that should be manufactured to maximize profit.

Test for relative maximum and minimum.

Test for relative maximum and minimum.

Test for relative maximum and minimum.

Suppose that the data in the table below shows the average earnings of year-round full-time workers by gender for several different levels of educational attainment. Find and interpret the slope of the linear regression line. Round the slope to three decimal places.

Test for relative maximum and minimum.