Problema Solution
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 $30 for each model A and $35 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) =
Answer provided by our tutors
The constrains are:
x + y <= 2500
100x + 150y <= 600,000
x >= 0
y >= 0
The objective function is p(x , y) = 30x + 35y. We need to find the maximum for p(x , y).
click here to see the graph of the system of inequalities and determine the corner points
the corner points are (2500, 0) and (0, 2500)
p(2500, 0) = 30*2500 = $75,000
p(0, 2500) = 35*2500 = $87,500
(x , y) = (0, 2500)
To maximize the profit National Business Machines should make 2500 units of model B.