1. Show a separate graph of the constraint lines and the solutions that satisfy each of the following constraints:

a. A ? 0.25 (A + B) b. B ? 0.10 (A + B) c. A ? 0.50 (A + B)

2. Identify the feasible region for the following set of constraints:

0.5A + 0.25B ? 30 1A + 5B ? 250 0.25A + 0.5B ? 50

A,B ?0

3. Identify the feasible region for the following set of constraints: 3A - 2B ?0 2A - 1B ?200 1A ? 50 A,B ?0

4. Consider the following linear program:

Max: 1A + 2B

s.t: 1A ?5

1B ? 4

2A + 2B =12

A,B ?0

a. Show the feasible region. b. What are the extreme points of the feasible region? c. Find the optimal solution using the graphical procedure.

5. Given the linear program

Max: 3A+4B

s.t: -1A + 2B ?8

1A + 2B ?1

2A + 1B ? 1

A,B ?0

a. Write the problem in standard form. b. Solve the problem using the graphical solution procedure. c. What are the values of the three slack variables at the optimal solution?

6. Consider the following linear program:

Max: 2A+ 3B s.t.: 5A + 5B ?400 Constraint 1 -1A + 1B ? 10 Constraint 2 1A + 3B ? 90 Constraint 3 A, B ? 0 Figure 2.22 shows a graph of the constraint lines. a. Place a number (1, 2, or 3) next to each constraint line to identify which constraint it represents. b. Shade in the feasible region on the graph. c. Identify the optimal extreme point. What is the optimal solution? d. Which constraints are binding? Explain. e. How much slack or surplus is associated with the nonbinding constraint?