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?
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?
1 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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