Question

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.

Answer 1

Sqdancefan's answer is correct.

Explanation:

I misread the question.

Answer 2

• 8 churches, 2 unions; $1350 per month

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 ≤ 20

and her limit on follow-up call hours is ...

x + 3y ≤ 14

Graphing 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