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Linear programming

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LINEAR PROGRAMMING : Some Worked Examples and Exercises for Grades 11 and 12 Learners. Example : A small business enterprise makes dresses and trousers. To make a dress requires 1 hour of 2 cutting and 20 minutes of stitching. To make a trousers requires 15 minutes of cutting and 1 hour of stitching. The profit on a dress is R40 and on a pair of trousers R50. The business operates for a 2 maximum of 8 hours per day. Determine how many dresses and trousers should be made to maximize profit and what the maximum profit is. Solution : Step 1 : To solve the above problem we would have to translate the conditions or constraints from a verbal to a symbolic form. We first introduce our variables. Let x be the number of dresses and y the number of trousers. Step 2 : Next we express the constraints as a system of inequalities . x ≥ 0 and y ≥ 0 , x and y being whole numbers ie. x , y∈ N0 Cutting Time: Stitching Time: 1 1 x + y ≤ 8 ie. 2x + y ≤ 32 2 4 1 1 x + y ≤ 8 ie. 2x + 3y ≤ 48 3 2 Step 3 : Graph the system of inequalities and shade in the region that satisfy the constraints. The shaded region is called the feasible region. y 32− 24− 16 − 8− 0 8 16 24 32 x ...
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