Linear programming

Question

National Business Machines manufactures x model A portable printers and y model B portable printers. Each model A costs $100 to make, and each model B costs $150. The profits are $40 for each model A and $35 for each model B portable printer. If the total number of portable printers demanded per month does not exceed 2500 and the company has earmarked no more than $600,000/month for manufacturing costs, how many units of each model should National make each month to maximize its monthly profit?

Answer 1

Since "x" is the number of model A printers and "y" is the number of model B printers then x + y < 2500 since the "total number . . . does not exceed 2500", You can also write this as y < -x + 2500

Since model A costs $100 to make then the cost to manufacture "x" printers is 100x and since model B printers costs $150 to make then the cost to manufacture "y" printers is 150y. Since "no more than $600,000/month" in cost is allocated then 100x + 150y < 600,000 or x + 1.5y < 6000 which can also be written as y < -2/3x + 4000

Graphing these:

We can see that the red curve governs the number of printers.

If you manufacture 0 model A's and 2500 model B's, then the profit will be:

P = (35)2500 = $87,500

If you manufacture 2500 model A's and 0 model B's, then the profit will be:

P = (40)2500 = $100,000

So to maximize the profit, it is best to manufacture 2500 model A's and zero model B's