Question

Consider the following Linear Programming model:

Maximize x+2.5y
Subject to

x+3y<=12

x+2y<=11

x-2y<=9

x-y>=0

x+5y<=15

x>=0

y>=0

(a) Draw the feasible region for the model, but DO NOT draw the objective function. Without graphing the objective function, find the optimal solution(s) and the optimal value. Justify your method and why the solution(s) you obtain is (are) optimal. (4 points)

(b) Add the constraint “x+5y>=15” to the Linear Programming model. Is the optimal solution the same as the one in (a)? If yes, justify your answer by highlighting the new feasible region. If not, provide the new optimal solution also by highlighting the new feasible region. In both cases, justify why the solution is optimal. (2 points)

Answer 1