The Shirt Shop manufactures and retails shirts in malls all over the city. Curre

Question

The Shirt Shop manufactures and retails shirts in malls all over the city. Currently, it is considering four (4) types of shirts to manufacture. Relevant pieces of infomation are as follows: Shirt B 34 10,000 200 0.12 0.25 0.10 2.5 500 0.25 0.07 Muscle Shirt 20 T-Shirt 25 7,000 Contribution/shirt Set-up cost Min. producton q Cutting Time Shirt A 30 8,000 300 0.10 0.20 0.07 0.05 0.10 0.02 0.08 0.15 0.03 1.75 Time (hours QC Time Materials (yards 700 0.10 0.06 Max. demand Em Silk screen 0.15 Other relevant inputs include the following a. Available resources are as follows: Cutting Hours -500 hours, Sewing Hours-1,000 hours, QC Hours 200 hours, materials 6,000 yards, embroidery hours 100 hours, and silkscreen hours-800 hours b. At least three types of shirts must be manufactured: c. Based on historic demands for shirts, the number of Muscle shorts and T-shirts manufactured should be at least twice the number of Sports Shirts A & B d. We will not manufacture any Sports Shirt A unless we have at least 800 units of muscle shirts and/or T-shirts: e. Similarly, we will not manufacture any Sports Shirt B unless we have at least 900 units of muscle shirts and/or T-shirts f. The total number of shirts made should not exceed 3,000 units; g. The total number of shirts made should at least be 1,500 units; h. Between Muscle shirts & T shirts, only 1 of them should have a production run of more than 700 units; and, i. Between Sports Shirts A and Sports Shirts B, only 1 of them should have a production run of more than 400 units. Formulate an ILP Model that will maximize operating profit fromthe manufacture of the shirts. Definition of variables Xi number of muscle shirts to make, I-binary variable for X X: = number of muscle shirts to make, I.-binary variable for X2 X-number of muscle shirts to make, I3-binary = number of muscle shirts to make, 14-binary variable for X4 I12 binary 134 binary variable for dichotomy between Sports shirt A & Sports shirt B All variable greater than our equal to zero variable for dichotomy between muscle shirts & T-shirts

Explanation / Answer

First Problem

Note: 'M' is a large number

Maximize X1 X2 X3 X4 I1 I2 I3 I4 I12 I34 RHS Obj. Function 20 25 30 34 -5000 -7000 -8000 -10000 Min. qty. X1 1 >= 400 Min. qty. X2 1 >= 500 Min. qty. X3 1 >= 300 Min. qty. X4 1 >= 200 Cutting Time 0.05 0.08 0.1 0.12 <= 500 Sewing Time 0.1 0.15 0.2 0.25 <= 1000 QC Time 0.02 0.03 0.07 0.1 <= 200 Materials 1.5 1.75 2.5 2.5 <= 6000 Demand X1 1 <= 800 Demand X2 1 <= 1200 Demand X3 1 <= 700 Demand X4 1 <= 500 Embroidery 0 0 0.1 0.25 <= 100 Silk screen 0.15 0.15 0.06 0.07 <= 800 Linking X1 1 -M <= 0 Linking X2 1 -M <= 0 Linking X3 1 -M <= 0 Linking X4 1 -M <= 0 Min. of 3 Types 1 1 1 1 >= 3 M&T vs. Sports 1 1 -2 -2 >= 0 M&T vs. Sports A 1 1 -M <= 800 M&T vs. Sports B 1 1 -M <= 900 Maximum Total 1 1 1 1 <= 3000 Minimum Total 1 1 1 1 >= 1500 Muscle vs. T (1) 1 -M <= 700 Muscle vs. T (2) 1 M <= 700 + M Sports A vs. B (1) 1 -M <= 400 Sports A vs. B (2) 1 M <= 400 + M

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