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A factory produces three products P, Q and R. Each product passes through three departments, which are fabrication, finishing and packaging. Each unit of product P requires 2, 4 and 2 hours respectively, Q requires 2, 4 and 5 hours respectively, while R requires 4, 3 and 4 hours respectively in 3 departments. In a day, 70 hours are available in fabrication department, 60 hours in finishing department and 100 hours in packaging department. The contribution of profit of each product are RM 12, RM 15 and RM 22 per unit respectively. The factory wishes to determine the product mix that will maximize the total profit. a) (i) Formulate a linear programming model. (ii) Solve the problem by using simplex method. (1) Obtain the optimal product mix and the maximum total profit.

A factory produces three products P, Q and R. Each product passes through three departments, which are fabrication, finishing and packaging. Each unit of product P requires 2, 4 and 2 hours respectively, Q requires 2, 4 and 5 hours respectively, while R requires 4, 3 and 4 hours respectively in 3 departments. In a day, 70 hours are available in fabrication department, 60 hours in finishing department and 100 hours in packaging department. The contribution of profit of each product are RM 12, RM 15 and RM 22 per unit respectively. The factory wishes to determine the product mix that will maximize the total profit. a) (i) Formulate a linear programming model. (ii) Solve the problem by using simplex method. (1) Obtain the optimal product mix and the maximum total profit.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
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A factory produces three products P, Q and R. Each product passes through three departments, which are fabrication, finishing and packaging. Each unit of product P requires 2, 4 and 2 hours respectively, Q requires 2, 4 and 5 hours respectively, while R requires 4, 3 and 4 hours respectively in 3 departments. In a day, 70 hours are available in fabrication department, 60 hours in finishing department and 100 hours in packaging department. The contribution of profit of each product are RM 12, RM 15 and RM 22 per unit respectively. The factory wishes to determine the product mix that will maximize the total profit. a) (i) Formulate a linear programming model. (ii) Solve the problem by using simplex method. (1) Obtain the optimal product mix and the maximum total profit. (2) By how much can the profit of a product Q change before it becomes profitable to change the optimal product mix?
Transcribed Image Text:A factory produces three products P, Q and R. Each product passes through three departments, which are fabrication, finishing and packaging. Each unit of product P requires 2, 4 and 2 hours respectively, Q requires 2, 4 and 5 hours respectively, while R requires 4, 3 and 4 hours respectively in 3 departments. In a day, 70 hours are available in fabrication department, 60 hours in finishing department and 100 hours in packaging department. The contribution of profit of each product are RM 12, RM 15 and RM 22 per unit respectively. The factory wishes to determine the product mix that will maximize the total profit. a) (i) Formulate a linear programming model. (ii) Solve the problem by using simplex method. (1) Obtain the optimal product mix and the maximum total profit. (2) By how much can the profit of a product Q change before it becomes profitable to change the optimal product mix?
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