Donna de paul is raising money for the homeless. she discovers that each church group requires 2 hours of letter writing and 1 hour of follow-up, while for each labor union she needs 2 hours of letter writing and 3 hours of follow-up. donna can raise $100 from each church group and $200 from each union local, and she has a maximum of 12 hours of letter writing and a maximum of 14 hours of follow-up available per month. determine the most profitable mixture of groups she should contact and the most money she can raise in a month.

a) 2 letters to church and 4 letters to union

b) $ 1000

Explanation:

Given data:

Letter writing time for church = 2 hours

Follow up required for church = 1 hour

Letter writing time for labor union = 2 hours

Follow up required for labor union = 3 hour

Funds from church = $ 100

Funds from union = $ 200

now, let the number of letters written to church be 'x'

and the number of letters written to labor union be 'y'

According to the given conditions

maximum timing for letter writing = 12 hours

thus,

2x + 2y ≤ 12 hours

or

x + y ≤ 6 hours   (1)

also,

Maximum time for follow up = 14 hours

thus,

1x + 3y ≤ 14 hours    (2)

thus, it becomes an LPP problem

on solving the both the equations as equation (1)

     x +   y = 6

- ( 1x + 3y = 14 )

    0 - 2y = -8

or

y = 4 hours

substituting the value of y in equation (1) we get

x + 4 = 6

or

x = 2

thus,

the most profitable mixture is 2 letters to church and 4 letters to labor union

now,

Most money that can be raised = (letters to church × money raise from the church) + (letters to union × money raise from the union)

on substituting the values, we have

Most money that can be raised = (2 × $ 100) + (4 × $ 200)

or

Most money that can be raised = $ 1000