### MATH 318, Chapter 7 Quiz

Name:
You may use a calculator on this quiz. You may not use a cell phone or computer. Please read each question carefully, show your work and give justifications for your answers. There are questions on both sides of this quiz paper.
1. (40 points) Consolidated Electronics has two employee training programs -- Leadership and Problem Solving. Management has determined that each Leadership seminar offered increases the company's productivity by 2% and each Problem Solving seminar offered inceases productivity by 1%.

Management plans to offer at least 25 seminars total, and they will offer no more than 25 of each type of seminar. Follow the steps described below to determine how many of each type of seminar to offer to maximize productivity.

Note: If you get stuck on a step, try to make a reasonable guess at the answer and use that guess in the next step. If your answer to part (b) is incorrect you can still get full credit on part (c) if your calculations are correct.

a) Formulate the linear programming problem that must be solved to answer this question.

b) Graph the feasible region for this problem.

c) Find the extreme points of this feasible region.

d) How many Leadership seminars should Consilidated Electronics offer? How many Problem Solving seminars should they offer? Why?

2. (20 points) In your own words, what is a constraint?

3. (20 points) Is the following linear programming problem unbounded or infeasible or does it have alternative optimal solutions? Pick one of the above and explain your choice.
 Max 40F + 30S s.t. F + S > 4 F > 2 S > 0 F > 0

4. (20 points) Which of the constraints in the previous problem is redundant? How do you know?