Linear Programming:

Solve the following linear programming problems.

(a) In a manufacturing process, the final product has a requirement that it must weigh exactly 150 kgs. The two raw materials used are A, with cost of Php 6 per unit and B, with a cost of Php 12 per unit. At least 15 units of B and no more than 20 units of A must be used. Each unit A weighs 4 kgs; each unit of b weighs 10 kgs. How much of each type of raw material should be used for each unit of final product to minimize cost? (b) Charot Polar Products makes downhill and crosscountry skis. A pair of downhill skis requires 2 man-hours for cutting, 1 man-hour for shaping and 3 man-hours for finishing while a pair of crosscountry skis requires 2 man-hours for cutting, 2 man-hours for shaping and 1 man-hour for finishing. Each day the company has available 140 man-hours for cutting, 120 man-hours for shaping and 150 man-hours for finishing. How many pairs of each type of ski should the company manufacture each day in order to maximize profit if a pair of downhill skis yields a profit of Php 10 and a pair of cross-country skis yields a profit of Php 8