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.

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.