Question 1

For a region, the percentage of adults 20-24 years of age that have not been married is given in the table below. Use the method of least squares to find the multivariable function f with inputs a and b for the best fitting line  where x is the number of years since 1970.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 2

The table shows the number of days that some food will keep as a function of the temperature. Use the method of least squares to find the best-fitting linear model for the data. Give your coefficients to two decimal places.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 3

Write the Lagrange system of partial derivative equations.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 4

Fatty acids are liberated from a fat mixture through a chemical process called hydrolysis. Suppose the number of fatty acids per 100 grams of water can be modeled by  grams, where the pH of the fat mixture is  and the temperature is  Find the pH and temperature that maximize the amount of fatty acid. Round your answers to two decimal place.

Accepted Answer

A)  pH: 4.12
Temperature:  
B)  pH: 6.22
Temperature:  
C)  pH: 0.71
Temperature:  
D)  pH: 6.34
Temperature:  
E)  pH: 6.06
Temperature:

Question 5

Let  be the SSE function for the best fitting line  of the data below. Find the minimum value of  Round your answer to four decimal places.

Accepted Answer

A)  0.000 
B)  0.0006 
C)  0.0188 
D)  0.8466 
E)  0.6648

Question 6

Consider the contour and associated three-dimensional graph of  Is the point at which  and  a relative maximum point, a relative minimum point, or a saddle point?

Accepted Answer

A)  saddle point 
B)  relative maximum 
C)  relative minimum

Question 7

For a region, the percentage of adults 20-24 years of age that have not been married is given in the table below. Give the linear model  that best fits this data, where x is the number of years since 1970.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 8

Locate and classify any critical points.

Accepted Answer

A)   , saddle point 
B)   , saddle point 
C)   , saddle point 
D)   , saddle point 
E)   , saddle point

Question 9

Let  be the SSE function for the best fitting line  of the data below. A student calculated that the minimum of f occurs at  . Based on this calculation, what is the linear function that best fits the data?

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 10

A travel agency offers spring-break cruise packages. The agency advertises a cruise to Cancun, Mexico, for $1200 per person. In order to promote the cruise among student organizations on campus, the agency offers a discount for student groups selling the cruise to over 50 of their members. The price per student will be discounted by $10 for each student in excess of 50. For example, if an organization had 55 members go on the cruise, each of those 55 students would pay  . Write a constraint function in terms of the number of students in excess of 50 and the price.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Exam 8: Analyzing Multivariable Change: Optimization

For a region, the percentage of adults 20-24 years of age that have not been married is given in the table below. Use the method of least squares to find the multivariable function f with inputs a and b for the best fitting line where x is the number of years since 1970.

The table shows the number of days that some food will keep as a function of the temperature. Use the method of least squares to find the best-fitting linear model for the data. Give your coefficients to two decimal places.

Write the Lagrange system of partial derivative equations.

Let be the SSE function for the best fitting line of the data below. Find the minimum value of Round your answer to four decimal places.

Consider the contour and associated three-dimensional graph of Is the point at which and a relative maximum point, a relative minimum point, or a saddle point?

For a region, the percentage of adults 20-24 years of age that have not been married is given in the table below. Give the linear model that best fits this data, where x is the number of years since 1970.

Locate and classify any critical points.

Let be the SSE function for the best fitting line of the data below. A student calculated that the minimum of f occurs at . Based on this calculation, what is the linear function that best fits the data?