Question : Need help with two math questions, stumped.?
1) A company manufactures two products, A and B, on two machines, I and II. It has been determined that the company will realize a profit of $ 3/unit of product A and $ 5/unit of product B. To manufacture a unit of product A requires 11 min on machine I and 7 min on machine II. To manufacture a unit of product B requires 19 min on machine I and 11 min on machine II. There are 5 hr of machine time available on machine I and 3 hr of machine time available on machine II in each work shift. How many units of each product should be produced in each shift to maximize the company’s profit?

2) National Business Machines manufactures two models of fax machines: A and B. Each model A costs $ 120 to make, and each model B costs $ 140. The profits are $ 29 for each model A and $ 43 for each model B fax machine. If the total number of fax machines demanded per month does not exceed 2700 and the company has earmarked no more than $ 500,000/month for manufacturing costs, how many units of each model should National make each month in order to maximize its monthly profit?

Thanks!
fax on demand

Best answer:

Answer by Geezah
1) Let A and B be the amount of units of product A and B that are being produced, respectively. Obviously, we need A >= 0 and B >= 0.

The profit is 3A + 5B. That’s what we want to maximize.

The amount of time used on machine I is 11 minutes for each “A” product and 19 minutes for each “B” product, so that’s 11A + 19B. This can’t exceed 5 hours, which is 300 minutes. So 11A + 19B <= 300. Likewise, for machine II we need to have 7A + 11B <= 180 minutes.

You have 4 inequalities. Now use linear programming to find the values of A and B that maximize 3A+5B.