Question

A factory 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?

Answer 1

@Michele_Laino

Answer 2

from the text of your problem, we have two inequalities, namely:
\[x+2y \le 1400, y \ge 100+x\]

Answer 3

ok, I didn't get this when it was covered over class...

Answer 4

please, note that if:
"The production of y must exceed the production of x by at least 100 units" I understand that
y>=100+x, do you agree?

Answer 5

yes that makes sense

Answer 6

furthermore, both x and y are positive quantities

Answer 7

yeah, so how do i find the vertices and max production?

Answer 8

so your region is defined by the subsequent inequalities:
y<=700-x/2,
y>=x+100
x>=0
y>=0