Question

A merchant plans to sell two models of MP3 players at costs of $250 and $300. The $250 model yields a profit of $25 per unit and the $300 model yields a profit of $40 per unit. The merchant estimates that the total monthly demand will not exceed 270 units. The merchant does not want to invest more than $73,500 in inventory for these products. What is the optimal inventory level for each model?

Answer 1

If there are x and y amounts of the two models, then
you want to maximize p = 25x + 40y
subject to the constraints
x+y <= 270
250x + 300y <= 73500
x >= 0
y >= 0
So graph these lines and evaluate p at each vertex to find the maximum profit