Problems:
1. Consider the following minimization problem.
Min z = x1 + 2x2
s.t. x1 + x2 ≥ 300
2x1 + x2 ≥ 400
2x1 + 5x2 ≤750
x1, x2 ≥ 0
Which constraints are satisfied at the optimal solution (x1 = 250, x2 = 50)?
2. Consider the following minimization problem.
Min z = 1.5x1 + 2x2
s.t. x1 + x2 ≥ 300
2x1 + x2 ≥ 400
2x1 + 5x2 ≤ 750
x1, x2 ≥ 0
What are the optimal values of x1, x2, and z ?
3. Consider the following linear programming problem:
Max Z = $15x + $20y
Subject to : 8x + 5y≤ 40
0.4x + y ≥4
x, y ≥0
Determine the values for x and y that will maximize revenue. Given this optimal revenue, what is the amount of slack associated with the first constraint?