The costs to a store 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 indicate the following constraints. The merchant estimates that the total monthly demand will not be exceed 200 units.
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 optimal profit?
A) A maximum profit of $4500 occurs when 180 of each model of GPS receiver is sold.
B) A maximum profit of $5000 occurs when 200 of each model of GPS receiver is sold.
C) A maximum profit of $5400 occurs when 180 of each model of GPS receiver is sold.
D) A maximum profit of $6000 occurs when 200 of each model of GPS receiver is sold.
E) A maximum profit of $5500 occurs when 100 of each model of GPS receiver is sold.

Question

Quizplus · Accepted Answer

The optimal inventory level can be found by setting up and solving a linear programming problem with the given constraints. The constraints are that the total units sold cannot exceed 200 and the total investment cannot exceed $18,000. The profit for each $80 model is $25 and for each $100 model is $30. By calculating the combination that maximizes profit without exceeding the constraints, we find that selling 100 of each model yields a profit of $25*100 + $30*100 = $5500, which fits within the investment limit of $18,000 ($80*100 + $100*100 = $18,000) and does not exceed the maximum units constraint of 200.

The Costs to a Store Two Models of Global Positioning