Introduction to mathematical programming
Introduction to mathematical programming
4th Edition
ISBN: 9780534359645
Author: Jeffrey B. Goldberg
Publisher: Cengage Learning
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Chapter 3.1, Problem 4P

Explanation of Solution

Reformulating LP to maximize Truckco’s profit:

From the given scenario, it is observed that a truck company manufactures two types of trucks 1 and 2. Each truck is assigned to go through the painting shop and assembly shop.

Let us consider,

If the paining shop were only paining Type 1 trucks, it could paint 800 per day.

If the paining shop were only paining Type 2 trucks, it could paint 700 per day.

If the assembly shop were only assembling truck 1, it could assemble 1500 per day.

If the assembly shop were only assembling truck 2, it could assemble 1200 per day.

  • x1 is the variable to represent the number of Type 1 Trucks produced daily.
  • x2 is the variable to represent the number of Type 2 Trucks produced daily.

The objective function is as follows:

Maximizez = 300x1+500x2

Considering the constraints,

Constraint 1: Paint shop constraint

Constraint 2: Engine ship constraint

Expressing the constraint 1 in terms of x1 and x2:

Type 1 truck paints 700 per day and Type 2 truck paints 800 per day

x1800+x2700

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Chapter 3 Solutions

Introduction to mathematical programming

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