CAPE Applied Mathematics Unit 2 · 2008 (second paper) · Paper 2 · Question 1(a)

A manufacturer produces two types of products, X and Y. X requires 6 man-hours per unit and Y requires 9 man-hours per unit, with 360 man-hours available per week. The manufacturing costs are 15 per unit for X and 9 per unit for Y, with a budget of 675 per week. The profit per unit is 15 for X and 27 for Y. Let P be the weekly profit and x and y be the number of units of X and Y produced weekly.

Formulate a linear programming model to determine the number of each product that maximizes the profit.