A manufacture makes two product, A and B. product A sells at each and takes hour to make. Product B sells at each and takes 1 hour to make. There is a permanent order for 14 of product and 16 of product B. A working week consist of 40 hours of production and the weekly turnover must not be less than \mp10000. If the profit on each of the product is and on product , it is then how many of each should be produced so that the profit is maximum? Also, find the maximum profit.

contexto.140

3 years ago

Let and be number of and products.
According to the question.

Maximize
The feasible region determined by is given by

The corner points of feasible region are .The value of at corner points are

The maximum value of is 1440 at point .
Hence, the manufacturer should manufacture 48 A products and products to maximize their profit of Rs. 1440 .