Problema Solution
A manufacturer of small copiers makes a profit of $200 on a deluxe model and $250 on a standard model. The company wants to produce at least 55 deluxe models per week and at least 60 standard models per week. However, the weekly production is not to exceed 155 copiers. How many copiers of each kind should be produced in order to maximize the profit?
Answer provided by our tutors
Let
x = the number of deluxe models
y = the number of standard models
x >=55
y >= 60
x + y <= 155
The objective function is the profit:
F(x, y) = 200x + 250y
First we need to find the corner points:
(55, 60), (95, 60) and (55, 100) are the corner points
Now we need to calculate the objective function into the corner points:
F(55, 60) = 200*55 + 250*60 = $26,000
F(95, 60) = 200*95 + 250*60 = $34,000
F(55, 100) = 200*55 + 250*100 = $36,000
In order to maximize the profit 55 standard and 100 deluxe models should be made.