Question

Efficient Homemakers Ltd. makes canvas wallets and leather wallets as part of a money making project. For the canvas wallets, they needtwo yards of canvas and two yards of leather. For the leather wallets, they need four yards of leather and three yards of canvas. Theirproduction unit has purchased 44 yards of leather and 40 yards of canvas. Let x be the number of leather wallets and y be the number ofcanvas wallets.The profit on a canvas wallet is $25 and the profit on a leather wallet is $40.What is the maximum profit?

A. $510
B. $250
C. $440
D. $550

Answer 1

To maximize profit, we need to determine the number of canvas wallets (y) and leather wallets (x) that will yield the highest profit. By graphing the feasible region and evaluating the profit function at each corner point, we find the maximum profit to be $550.

Step-by-step explanation:

To maximize profit, we need to determine the number of canvas wallets (y) and leather wallets (x) that will yield the highest profit. Let's set up the equations based on the given information:For canvas wallets: 2y yards of canvas and 2y yards of leatherFor leather wallets: 4x yards of leather and 3x yards of canvasWe also know that the production unit has purchased 44 yards of leather and 40 yards of canvas.By setting up the equations:2y + 4x ≤ 44 (equation 1)2y + 3x ≤ 40 (equation 2)To maximize profit, we need to determine the region where both equations are satisfied. Graphically, the region where both inequalities hold true represents the feasible region.After graphing the feasible region, we identify the corner points which represent the potential maximum profit points. Evaluating the profit function at each corner point, we find the maximum profit to be $550.