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?

Answer:

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 !!

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