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 $250 from each union. She has a maximum of 16 hours of letter writing and 12 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.

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Business

Kailey Proctor

18 February, 15:58

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 $250 from each union. She has a maximum of 16 hours of letter writing and 12 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.

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Alessandra Vincent · Answer 1

6 cruch and 2 labor

provides 6 x 125 + 2 x 250 = 1,250

Explanation:

2x + 1y = 125

2x + 3y = 250

contribution per letter writing:

125 / 2 = 75

250 / 2 = 125

contribution per call hour:

125 / 1 = 125

125 / 3 = 41.67

The church provides better yield per constrain resourse so first we use church

maximum church group possible:

letters 16/2 = 8

calls 12 / 1 = 12

the maximum amount possible is 8 but doing so

leave unsued capacity for the follow-up calls.

Therefore is better to reduce the cruch meetings to use the entire capacity leaving a combination of:

6 church x 2 letter = 12

2 labor union x 2 letter = 4

total 16

6 church x 1 hs call = 6

2 labor union x 3 hs call = 6

total 12