Question

Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. HINT [See Example 1.] (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.)

Minimize c = −x + 5y subject to

y ≤
2x
3
x ≤ 3y
y ≥ 4
x ≥ 6
x + y ≤ 16.
c =
(x, y) =

Answer 1

8

Explanation:

Minimize c = -x + 5y

The constraints say

2x >= 3y, x<=3y, y>=4 and x>=6, x+y<=12

Since we need to minimize y and maximize x in order to minimize c

y_(min) = 4

x_(max) <= 3y_(min) <= 12

which is also a constraint from x + y <= 16

Hence the closest feasible solution will be (12,4)

Therefore, minimum value of c will be -12 + 5(4) = 8

Hence the final answer is equal to 8