# Linear Programming & Method of Elimination

I need help with the following problems. As much detail you can give me to help me understand how to work the problems would be great.

1. Henry is raising money for the homeless animals, and discovers each shelter requires 2 hours of volunteer service and 1 hr of contacting possible owners, which each homeless shelter needs 4 hours of volunteer service and 3 hr of follow-up. He can raise $100 for each animal shelter and $150 for each homeless shelter. Henry has a maximum of 10 hours of volunteer time and 13 hours of contacting time each month. Determine the most profitable mixture of groups he should contact and the most money he can raise in a month.

Set this up in a linear programming. How many animal shelters and homeless shelters should he contact and what should he collect in donations.

Graph:

Minimize: z = 5x + y

Subject to: 4x + 4y ≥ 16

4x + y ≥ 19

With x ≥ 0 and y ≥ 0

Minimize z=_______with (x,y) = _________________

I tried to do the following problem but am confused:

Solve the following system by the Method of Elimination:

2x - 4y = 40

5x + 3y = -17 (x, y) = ___________________________

7x - y = 57

Suppose that the national demand and price for a certain type of energy-efficient exhaust fan are related by p = D(q) = 495 - q, where p is the price (in dollars) and q is the demand (in thousands).

Can you please check the answers below and let me know. I am starting to doubt my answers.

If the demand is for 80,000 exhaust fans, then the price equals $960.00

(6/5)*80000 = 9600

At a price of $141, the demand is for _140___thousand exhaust fans.

141 - (6/5) = 139.8

#### Solution Summary

The solution provides step by step method for the calculation of optimal solution for a maximization and minimization problem using graphical method. The solution also provides step by step method for the method of elimination. Graph of the feasible region is also included.