A factory cam 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 200 units. Moreover, production levels are limited by the formula x+2y≤1600. What production levels yield maximum profit?

Solution : - Given a factory can produce two products x and y with profit approximated by p (x) = 14 x + 22 y - 900

The production of y can exceed x by no more than 200 units. So the required constraints are

y - x < 200 [equation 1]

We draw the graph of equation 1 using table 1 as shown in figure.

and

x + 2 y ≤ 1600 [equation 2]

We draw the graph of equation 2 using table 2 as shown in figure.

Total profit p (x) = 14 x + 22 y - 900

The mathematical formulation of the given problem is

Maximize p (x) = 14 x + 22 y - 900

Subject to the constraints

y - x < 200 x + 2 y ≤ 1600 As we can see the table 3 the maximum profit is $21500 at (1600,00). So a production of 1600 of x and 0 of y gives the maximum profit of $21500