Question: Given this linear programming Model: Max Z = 12x + 16y (profit) s.t. (1) 10x + 20y < 140 (2) 20x + 16y < 180

Given this linear programming Model:

Max Z = 12x + 16y (profit)

s.t.

(1) 10x + 20y < 140

(2) 20x + 16y < 180

(3) 12x + 12y < 120

(4) x,y > 0

(a) Solve the problem by the graphical method.

(b) What would be the optimal solution if the objective function had been 16x + 8y?

(c) What would be the optimal values be if the constraint had been (3) 12x + 12y < 180 instead of (3) 12x + 12y < 120?

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