# A factory can produce two products, x and y, with a profit approximated by P = 14x + 22y – 900?

A factory can produce two products, x and y, with a profit approximated by P = 14x + 22y – 900?

The production of y can exceed x by no more than 100 units. Moreover, production levels are limited by the formula x + 2y ≤ 1,400. What production levels yield maximum profit?

by
selected by

P = 14x + 22y – 900

x + 2y ≤ 1,400

y ≤ x + 100

so

y ≤ 700 - x/2 ( intercept: 700, slope -1/2)

y ≤ x + 100 ( intercept: 100, slope 1)

the extrema is reached at an edge of the domain

which is a triangle

y = 700 - x/2

y = x + 100

intersection at

x + 100 = 700 - x/2

3/2 x = 600

x = 2/3 * 600

x = 400

and

y = 400 + 100 = 500

as P is an increasing function for

of course positive values of x and y

the maximum is reached for

x = 400

y = 500

hope it'll help !!

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat.

+1 vote