Quick-Print Limited is a clothing manufacturing company that specializes in producing commemorative shirts immediately following major sporting events like the World Cup, Asian Games etc. The company has been contracted to produce garments for the winning cricket team in the coming World Cup.
The items produced include two types of sweatshirts, one with silk screen printing on the front (F) and one with print on both back and front sides (B/F), and two types of T-shirts of the same configuration (F and B/F).
The company has to complete all production within 48 hours after the game, at which time a trailer truck will pick up the shirts. The company will work around the clock. The truck has enough capacity to accommodate 1,400 standard-size boxes. A standard-size box holds 12 garments. The company has budgeted Rs. 125,000 for the production run.
The resource requirements, unit costs, and profit for each type of shirt are shown in the following table.
Processing Time (hr)
Cost (Rs)
Profit (Rs)
Sweatshirt–F
0.22
36
90
Sweatshirt–B/F
0.36
48
126
T-shirt–F
0.06
26
44
T-shirt–B/F
0.32
38
62
The company wants to know how many units of each type of shirt to produce in order to maximize the total profit.
Formulate the above problem as a Linear Program.
NOTE: Clearly define the variables and label each constraint.
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