# Algebra

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?

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1. What does this constraint mean?

limited by the formula x+2y,+1,400.

I have to leave, hope Steve sees this.

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posted by Damon
2. Constraints:
A. x≥0
B. y≥0
C. y-x≤100
D. x+2y≤1400 (please check this constraint)

Draw the graph of the constraint equation to have a visual understanding.

Solve for all possible corners of the feasible polygon. Note that all inequalities are inclusive, i.e. all lines are part of the feasible region.
A/B: (0,0)
A/C: (0,100)
A/D: - (y-x>100)
B/C: - (x<0)
B/D: (1400,0)
C/D: (650,750)

Since the feasible polygon is necessarily convex, we only have to check profit at the intersections.

P(x,y)=14x+22y-900
P(0,100)=1300
P(1400,0)=18700
P(650,750)=24700

So the maximimum profit can be attained by X=650, Y=750.

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posted by MathMate

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