Find the maximums and minimums of $z = 15x+14y$ with constraints $0 \leq x \leq 10, 0 \leq y \leq 5, 3x+2y \geq 6$
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?
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.