Question: Solve the following linear programming model using graphic paper (you do not need to submit your graph): Maximize P = 9 X + 3 Y

Solve the following linear programming model using graphic paper (you do not need to

submit your graph):

Maximize P = 9 X + 3 Y

Subject to 20 X + 30 Y < 300

10 X + 5 Y < 80

X > 0

Y > 2 (pay attention to this constraint)

(a) Plot each constraint to determine the feasible region and label it.

(b) Plot the objective function and identify the optimal point (hint: try P = 27)

(c) What are the optimal solutions for X and Y and what is the maximum profit?

X* = Y* = P* =

(d) If a new constraint, X > 3, is added to the model, will this new constraint change

a) the feasible region? Yes ( ) No ( )

b) the optimal solutions for X and Y? Yes ( ) No ( )

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