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 ?$150 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

Jayanta needs 2 labor union groups and 8 church groups.

Explanation:

Let c denotes churches .

Let l denotes labor unions.

We know that Jayanta can only spend 20 hours letter writing and 14 hour of follow-up.

So, equations becomes:

`2c+2l=20`

`c+3l=14`

And total money raised can be shown by =
`150c+175l`

We have to maximize
`150c+175l` keeping in mind that
`2c+2l \leq 20` and
`c+3l \leq 14`

We will solve the two equations:
`2c+2l=20` and
`c+3l=14`

We get l = 2 and c = 8

And total money raised is
`150*8 + 175*2` =
`1200+350=1550` dollars.

Hence, Jayanta needs 2 labor union groups and 8 church groups.