Donna de paul is raising money for the homeless. She discovers that each church group requires 2 hours of let her writing and 1 hour of follow-up while for each labor union she needs 2 hours of letter written and 3 hours of follow-up. Donna can raise $150 from each church group and $200 from each Union Local and she has a maximum of 20 hours of letters written and a maximum of 16 hours of follow-up available per month. Determine the most profitable mixture of group she should contact in the most money she can lose in a month.

z = () x1 + () x2

x = 7

y = 3

z (max) = 4950/3 = 1650

Step-by-step explanation:

Let call

x numbers of church goup and

y numbers of Union Local

Then

First contraint

2*x + 2*y ≤ 20

Second one

1*x + 3*y ≤ 16

Objective Function

z = 150*x + 200*y

Then the system is

z = 150*x + 200*y To maximize

Subject to:

2*x + 2*y ≤ 20

1*x + 3*y ≤ 16

x ≥ 0 y ≥ 0

We will solve by using the Simplex method

z - 150 * x - 200*y = 0

2*x + 2*y + s₁ = 20

1*x + 3*y + 0s₁ + s₂ = 16

First Table

z x y s₁ s₂ Cte

1 - 150 - 200 0 0 = 0

0 2 2 1 0 = 20

0 1 3 0 1 = 16

First iteration:

Column pivot (y column) row pivot (third row) pivot 3

Second table

z x y s₁ s₂ Cte

1 - 250/3 0 0 200/3 = 3200/3

0 - 4/3 0 - 1 2/3 = - 20/3

0 1/3 1 0 1/3 = - 20/3

Second iteration:

Column pivot (x column) row pivot (second row) pivot - 4/3

Third table

z x y s₁ s₂ Cte

1 0 0 750/12 700/6 = 4950/3

0 1 0 3/4 - 1/2 = 7

0 0 1 - 1/4 1/2 = 9/3