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28 September, 22:41

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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  1. 29 September, 00:11
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    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
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