Question

1. Optimal Profit

The costs to a store for two models of Global Positioning System (GPS) receivers are $80 and $100. The $80 model yields a profit of $25 and the $100 model yields a profit of $30.

Market tests and available resources determined the constraints below.

(a) The merchant estimates that the total monthly demand will not exceed 200 units.

(b) The merchant does not want to invest more than $18,000 in GPS receiver inventory.

What is the optimal inventory level for each model? What is the optimal profit?

2. Optimal Profit

A fruit grower has 150 acres of land for raising crops A and B. The profit is $185 per acre for crop A and $245 per acre for crop B.

Research and available resources determined the constraints below.

(a) It takes 1 day to trim an acre of crop A and 2 days to trim an acre of crop B, and there are 240 days per year available for trimming.

(b) It takes 0.3 day to pick an acre of crop A and 0.1 day to pick an acre of crop B, and there are 30 days per year available for picking.

What is the optimal acreage for each fruit?  What is the optimal profit?

Answer 1

Solution:

1)

2)