Financial and Finite Math question......(word problem).

Question

National Business Machines manufactures 2 models of fax machines: A and B. Each model A costs $100 to make, and each model B costs $150. The profits are $30 for each model A and $40 for each model B. If the total number of fax machines per month does not exceed 2500 and the company has earmarked no more than $600,000 per month for manufacturing costs, how many units of each model should National make each month in order to maximize its monthly profits? What is the optimal profit?

Answer 1

100A+150B </=600,000

2A +3B </= 12,000, (6,000, 0), (0,4,000)

A+B</=250 (250,0), (0,250)

max 30A+40B

graph 2nd & 3rd inequalities, A on vertical axis, B on horizontal. find the vertices of the enclosed area

(0,0), (250,0), (0,250)

40(250) - 150(40) = 4,000

30(250) -100(30) = $4,500 is maximum profit with 250 A and 0 B