Jayanta is raising money for the homeless, and discovers each church group requires 2 hr of letter writing and 1 hr of follow-up calls, while each labor union needs 2 hr of letter writing and 3 hr of follow-up. She can raise $125 from each church group and $175 from each union. She has a maximum of 20 hours of letter writing and 14 hours of follow-up available each month. Determine the most profitable mixture of groups she should contact and the most money she can raise in a month.
Accepted Solution
A:
Answer:8 churches, 2 unions; $1350 per monthStep-by-step explanation:Let x and y represent the numbers of churches and unions contacted in the month, respectively. Then Jayanta's limit on letter writing hours is ... 2x +2y ≤ 20and her limit on follow-up call hours is ... x + 3y ≤ 14Graphing these inequalities (see below) results in a feasible region with vertices at (x, y) = (0, 4 2/3), (8, 2), and (10, 0). Of these, the mixture of groups producing the most money is ... 8 churches and 2 unions.The money she can raise from that mixture is ... 8×$125 +2×$175 = $1350 in a month