Mathematics, 26.06.2019 04:30 noahrdavila1978

Afactory can produce two products, x and y, with a profit approximated by p=14x+22y-900. the production of y must exceed the production of x by at least 100 units. moreover, production levels are limited by the formula x+2y< 1400. a) identify the vertices of the feasible region. b) what production levels yield the maximum profit, and what is the maximum profit?

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Answer from: heidibode

When profits are maximized, it means we want to get the highest possible profit from a function.

The vertices of the feasible region are: $\mathbf{(x,y) = \{(0,100), (0,700),(400,500)\}}$ The production level that yields maximum profit is x = 400; y = 500

The maximum profit is #17100

Production of y must exceed x by 100 means

y x + 100

The production level is given as:

x + 2y < 1400

Since x and y represent products, then:

x, y 0

So, we have:

P = 14x + 22y - 900 --- the objective function

Subject to

y x + 100

x + 2y < 1400

x, y 0

See attachment for the graph of the subjects

(a) The vertices of the feasible region

From the attached image, the vertices of the feasible region are:

$\mathbf{(x,y) = \{(0,100), (0,700),(400,500)\}}$

(b) The maximum profit

Recall that: x, y 0

This means that, we can only make use of:

$\mathbf{(x,y) = \{(400,500)\}}$

So;

The production levels that yield maximum profit are:

x = 400; y = 500

Substitute these values in P = 14x + 22y - 900 , to calculate the maximum profit

P = 14x + 22y - 900

$P = 14 \times 500 + 22 \times 500 - 900$

P = 17100

Hence, the maximum profit is: #17100

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