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 ​$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.

Answer 1

Answer:

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