Name:    Chapter 6 Post Test

1.

Solve the system by the method of substitution.

 a. b. c. d. e.

2.

Solve the system graphically.

 a. b. c. d. e.

3.

Solve the system by the method of elimination and check any solutions algebraically.

 a. b. c. d. e.

4.

Solve the system by the method of elimination.

 a. b. (dependent) c. d. inconsistent e.

5.

Find the least squares regression line for the points

by solving the system for a and b.

Points:
 a. y = 3.93x –4.21 b. y = 2.80x –3.20 c. y = –2.66x +2.80 d. y = –3.47x –4.21 e. y = –3.20x +2.80

6.

Use back-substitution to solve the system of linear equations.

 a. b. c. d. e.

7.

Find the equation of the circle that passes through the points.

 a. b. c. – d. e.

8.

Find values of x, y, and that satisfy the system. These systems arise in certain optimization problems in calculus, and is called a Lagrange multiplier.

 a. b. c. d. e.

9.

A chemist needs 10 liters of a 25% acid solution. The solution is to be mixed from three
solutions whose concentrations are 10%, 20%, and 50%. How many liters of each solution will satisfy each condition? Use 2 liters of the 50% solution.
 a. 2 L of 10%, 7 L of 20%, 1 L of 50% b. 7 L of 10%, 7 L of 20%, 2 L of 50% c. 7 L of 10%, 1 L of 20%, 2 L of 50% d. 1 L of 10%, 2 L of 20%, 7 L of 50% e. 1 L of 10%, 7 L of 20%, 2 L of 50%

10.

Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants.

 a. b. c. d. e.

11.

Write the partial fraction decomposition of the rational expression. Check your result algebraically.

 a. b. c. d. e.

12.

Write the partial fraction decomposition of the rational expression. Check your result algebraically.

 a. b. c. d. e.

13.

Write the partial fraction decomposition of the rational expression.

 a. b. c. d. e.

14.

Select the correct graph of the inequality.

 a. d. b. e. c.

15.

Find the consumer surplus and producer surplus.

Demand

Supply
 a. Consumer surplus: Producer surplus: b. Consumer surplus: Producer surplus: c. Consumer surplus: Producer surplus: d. Consumer surplus: Producer surplus: e. Consumer surplus: Producer surplus:

16.

Find the minimum value of the objective function and where they occur, subject to the indicated constraints.

Objective function:

Constraints:

 a. Minimum at b. Minimum at c. Minimum at d. Minimum at e. Minimum at

17.

Select the region determined by the constraints. Then find the minimum value of the objective function (if possible) and where they occur, subject to the indicated constraints.

Objective function:

Constraints:

 a. Minimum at d. Minimum at b. No minimum e. Minimum at c. Minimum at

18.

Find the maximum value of the objective function and where they occur, subject to the constraints:

Objective function:

Constraints:

 a. Maximum at 80 b. Maximum at c. No maximum d. Maximum at e. Maximum at

19.

The linear programming problem has an unusual characteristic. Select a graph of the solution region for the problem and describe the unusual characteristic. Find the maximum value of the objective function (if possible) and where they occur.

Objective function:

Constraints:

 a. The constraint is extraneous. Maximum at d. The constraint is extraneous. Maximum at b. The constraint is extraneous. Maximum at e. The constraint is extraneous. No maximum. c. The constraint is extraneous. Maximum at

20.

An accounting firm has 780 hours of staff time and 272 hours of reviewing time available each week. The firm charges for an audit and for a tax return. Each audit requires 60 hours of staff time and 16 hours of review time. Each tax return requires 10 hours of staff time and 4 hours of review time. What numbers of audits and tax returns will yield an optimal revenue? What is the optimal revenue?
 a. 0 audit16 tax returnsOptimal revenue: b. 13 audits0 tax returnOptimal revenue: c. 16 audits0 tax returnOptimal revenue: d. 0 audit13 tax returnsOptimal revenue: e. 10 audits10 tax returnsOptimal revenue: