SOLUTION: Hi, Need some help on this question. It's a practice test question and I'm a bit confused. Graph the following system and solve the linear programming problem: Maximize: P=7

Question 203167: Hi,
Need some help on this question. It's a practice test question and I'm a bit confused.
Graph the following system and solve the linear programming problem:
Maximize: P=7x+10y
subject to: {2x+5y<=80
{4x+3y<=104
x>=0; y>=0
Thank you!
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Graph the two lines. Note that (0,0) is in the solution set for both of them, hence the solution set for each of the inequalities is the half-plane region below and to the left of the graphed line. The two non-negative constraints further bound the area of feasibility to above and to the right of the coordinate axes. See graph:

Considering the two non-negative constraints, the area of feasibility is the quadrilateral region bounded by the two coordinate axes, the green graph line on the top and the red graph line on the right.

The proof is beyond the scope of this discussion, so take it on faith that the optimum point will be one of the vertices of the feasibility area, namely: (0,0), (0,16), (26,0), or (20, 8).

Substitute the coordinate values for the 4 possible optimum points into your objective function and see which one has the maximum result.

You can calculate the other two and decide which is maximum.

John

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