Solve the problem.
-Mrs. White wants to crochet hats and afghans for a church fundraising bazaar. She needs 5 hours to make a hat and 4 hours to make an afghan, and she has no more than 51 hours available. She has material for no
More than 12 items and no more than 10 afghans. The bazaar will sell the hats for $20 each and the afghans
For $8 each. How many of each should she make to maximize the income for the bazaar? What is the
Maximum income?
A)3 hats and 9 afghans; $132
B)9 hats and 3 afghans; $204
C)10 hats and 2 afghans; $216
D)5 hats and 7 afghans; $156

Question

Quizplus · Accepted Answer

The correct answer is A) 3 hats and 9 afghans; $132.Let x be the number of hats and y be the number of afghans.Objective function: Maximize income = 20x + 8yConstraints:5x + 4y ≤ 51 (time constraint)x + y ≤ 12 (material constraint)x ≤ 10 (afghan constraint)y ≤ 10 (hat constraint)x ≥ 0, y ≥ 0 (non-negativity constraints)Solving the constraints, we get:0 ≤ x ≤ 100 ≤ y ≤ 100 ≤ x + y ≤ 120 ≤ 5x + 4y ≤ 51Graphing the constraints, we find that the feasible region is a quadrilateral with vertices (0, 0), (10, 0), (10, 2), and (0, 10).Evaluating the objective function at each vertex, we get:(0, 0): income = 0(10, 0): income = 200(10, 2): income = 216(0, 10): income = 80The maximum income is $216, which occurs when x = 10 and y = 2. Therefore, Mrs. White should make 10 hats and 2 afghans to maximize the income for the bazaar.

Solve the Problem. -Mrs. White Wants to Crochet Hats and Afghans for a Afghans