# linear practie - LINEAR PROGRAMMING Some Worked Examples...

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1 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 2 1 hour of cutting and 20 minutes of stitching. To make a trousers requires 15 minutes of cutting and 2 1 hour of stitching. The profit on a dress is R40 and on a pair of trousers R50. The business operates for a 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 . 0 y and 0 x , x and y being whole numbers ie. y , x N 0 Cutting Time: 32 y 2x ie. 8 y 4 1 x 2 1 + + Stitching Time: 48 y 3 2x ie. 8 y 2 1 x 3 1 + + Step 3 : Graph the system of inequalities and shade in the region that satisfy the constraints. The shaded region is called the feasible region . Step 4: Write the profit in terms of the variables. P = 40x + 50y Since the objective (in this case) is to make a maximum profit, the profit equation is called the objective function . Step 5: To determine the maximum profit and the number of items that will give the maximum profit we can use one of two methods : 5.1 Substitute each of the ordered pairs of the vertices of the feasible region, excluding (0;0) , ie. (0;16) , (16;0) and (12;8) into profit equation .

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• Summer '15
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• Binary relation, Ordered pair, 8 hours, 4 hours, 5 hours

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