The Brooktronics Company has a contract to produce 5000 led Christmas light disp

Question

The Brooktronics Company has a contract to produce 5000 led Christmas light displays for a large discount chain (Sprawl-Mart). Brooktronics can produce 4 different types of displays and the chain wants at least 3 different types of displays in the order. There is a fixed set-up cost that must be incurred whenever machinery is converted to produce a different display type. Profit data and capacity for each display type are below 9· Capacity Fixed Cost to Set Up Production Run 750 500 300 800 Profit per Per display 10.00 15.00 20.00 25.00 Display type 1 (Rudolph) 2 (Elf) 3 (Santa) 2000 1200 1800 1000 4 (Nativity Scene) Write a mixed-integer linear programming model for this problem in the space below Assume Brooktronics wants to maximize total profit, and yet produce enough bulbs to meet Sprawl-Mart's 5000 display demand. a.

Explanation / Answer

MILP model

Let  

Xi = 1, if display type "i" is produced, otherwise Xi = 0, where i = 1,2,3,4

Yi = Quantity of display type "i" produced, where i = 1,2,3,4

Objective: Max 10Y1 + 15Y2 + 20Y3 + 25Y4 - 750X1 - 500X2 - 300X3 - 800X4

s.t.

X1 + X2 + X3 + X4 >= 3   (at least 3 display types to be produced)

Y1 + Y2 + Y3 + Y4 = 5000 (order for 5000 displays)

2000X1 - Y1 >= 0 (capacity constraint of display type 1)

1200X2 - Y2 >= 0 (capacity constraint of display type 2)

1800X3 - Y3 >= 0 (capacity constraint of display type 3)

1000X4 - Y4 >= 0 (capacity constraint of display type 4)

Xi = 0,1   (binary variable)

Yi >= int   (integer)

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