National Business Machines manufactures x model A fax machines and y model B fax

Question

National Business Machines manufactures x model A fax machines and y model B fax machines. Each model A costs $100 to make, and each model B costs $150. The profits are $45 for each model A and $50 for each model B fax machine. If the total number of fax machines 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?

(x,y)= ?

What is the optimal profit?

Explanation / Answer

Constraints are

x + y <= 2500

100x + 150y <= 600000

Profit Function Z = 45x + 50y

Dividing the second equation by 50 we get the second constraints as

2x + 3y <= 12000

Finding the intersection point of two constraints we get y=7000,x=-4500, hence we can manufactures, the machines which will maximize the profit

Hence we will produce 0x machines and 2500 y machines

Optimal coordinate = (0,2500)

Optimal Profit = 45(0) + 50(2500) = $125,000

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