Find the maximums and minimums of z = 15 x + 14 y with constraints 0 &#x2264;<!

Scott Martinez

Scott Martinez

Answered question

2022-06-02

Find the maximums and minimums of z = 15 x + 14 y with constraints 0 x 10 , 0 y 5 , 3 x + 2 y 6
I obviously can't take the partial derivatives of inequalities, so I'm at a loss here as my brain simply can't analyze/visualize 3 simultaneous constraints on the graph at once. What is the easiest/most efficient way of analyzing this system?

Answer & Explanation

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a1p2ung1ls6t7

Beginner2022-06-03Added 6 answers

This is a linear programming problem.
Step 1: graph the constraints.
Step 2: find any corner points.
Step 3: evaluate z at the corners.
Step 4: pick winners and losers.
Alternatively, parameterize the boundary and apply the closed interval method on each boundary segment. But, given that the objective function is linear this hardly seems necessary.

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