Question

The Fallen Flags Division of Block C Enterprises makes toy trucks and cars by a plastic molding process. The panel truck requires 3 minutes of molding time, 2 minutes of painting time and 1 minute of packing time. The pickup truck requires 2.5 minutes of molding time, 3 minutes of painting time and 1 minute of packing time. The car requires 1.5 minutes of molding time, 1.5 minutes of painting time and 1 minutes of packing time. There are a total of 3000 minutes of molding time, 2000 minutes of painting time and 1800 minutes of packing time each day. Each car or truck contributes $1 per unit to profit. In addition, the number of trucks must be no greater than the number of cars and a minimum of 100 of each vehicle must be produced. Determine the mix of trucks and car that will maximize profit.

Answer 1

Let T1, T2, and C be the number of Panel Trucks, Pickup Trucks, and Cars respectively to be produced.

Maximize Z = total profit = 1T1 + 1T2 + 1C
Subject to,
3.0T1 + 2.5T2 + 1.5C <= 3000 (molding time)
2.0T1 + 3.0T2 + 1.5C <= 2000 (painting time)
1.0T1 + 1.0T2 + 1.0C <= 1800 (packing time)

T1 + T2 - C <= 0

T1 >= 100; T2 >= 100; C >= 100

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