Suppose the feasible region has four corners, at these points: (0, 0), (5, 0), (0, 4), and (2, 3). For which of these profit formulas is the profit maximized, producing a mix of products at (2, 3)?
A) $4x + $3y
B) $3x + $4y
C) $1x + $3y
D) $2x + $1y

Question

Quizplus · Accepted Answer

We need to find the profit formula for which the solution at (2,3) produces the maximum profit. We can plot the feasible region and draw the lines for each profit formula. Then we can check which line intersects the feasible region at the point (2,3) and has the maximum value at that intersection point.

After plotting the feasible region, we can see that the lines for profit formula B (3x + 4y) and D (2x + y) intersect at (2,3), but the line for formula B has a higher value at that point. Therefore, the profit is maximized using profit formula B.

Suppose the Feasible Region Has Four Corners, at These Points