2) (33 points) Formulate the following mathematical program (do not solve). Gra

Question

2) (33 points) Formulate the following mathematical program (do not solve). Gra Enterprises (GKE to make each type of ball must be rented ($200/week-blue; $150/week-yellow; and $100/week-red). To produce these balls labor and plastic are required as shown below ) can produce 3 different color keno balls (blue, yellow and red). The machinery Labor (hours) Plastic (cubic meters) Blue 3 Yellow 2 Red 6 Each week 150 hours of labor are available and 160 cubic meters are available. The unit cost and selling price is shown below: Variable Cost $6 $4 $8 Sales Price Blue $12 Yellow $8 Red $15 Formulate this problem to maximize GKE's weekly profits

Explanation / Answer

Mathematical model

Decision variables:

Y1 is a binary variable such that Y1 = 1, if machinery is rented to make Blue balls

Y2 is a binary variable such that Y2 = 1, if machinery is rented to make Yellow balls

Y3 is a binary variable such that Y3 = 1, if machinery is rented to make Red balls

X1 = Number of Blue balls to be produced per week

X2 = Number of Yellow balls to be produced per week

X3 = Number of Red balls to be produced per week

Objective: Max (12-6)*X1 + (8-4)*X2 + (15-8)*X3 - 200Y1 - 150X2 - 100X3

s.t.

M*Y1 - X1 >= 0   (where M is a hypothetically large number, say 1000)

M*Y2 - X2 >= 0

M*Y3 - X3 >= 0

3X1 + 2X2 + 6X3 <= 150

4X1 + 3X2 + 4X3 <= 160

X1, X2, X3 >= 0

Y1, Y2, Y3 = 0.1

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