Answer:
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
