Linear Programming Model Problem!!

This problem is giving me a headache, i've been working on it for 2 days:


"Bill's Grill is a popular college restaurant that is famous for its hamburgers. The owner of the restaurant, Bill, mixes fresh ground beef and pork with a secret ingredient to make delicious quarter-pound hamburgers that are advertised as having no more than 25% fat. Bill can buy beef containing 80% meat and 20% fat at $0.85 per pound. He can buy pork containing 70% meat and 30% fat at $0.65 per pound. Bill wants to determine the minimum cost way to blend the beef and pork to make hamburgers that have no more than 25% fat.

a) formulate an LP Model for this problem (Hint: The decision variables for this problem represent the percentage of beef and the percentage of pork to combine.)"
b) sketch the feasible region for this problem
c) determine the optimal solution to this prob by enumerating the corner points


now for "a" this is what i put please help (a part that is messing me up is it says quarter pounder hamburger, and then they're ordering pounds that shouldn't matter right?)

a)
MIN: .85x1 + .65x2
S.T. .20x1 + .30x2 <=.25
x1, x2 >0
x1 + x2 = 1
This is the part where im screwing up, not sure if those constraints are correct especially the last one, i was trying to make it = 100% not sure if that is needed.

Please Help

anyone able to help me?

Your constraint and objective look fine to me. Just looking at the problem, we can see if we mix 50-50 at $0.75/lbs we will get the optimum.


But, see here:

http://arstechnica.com/civis/viewtopic.php?f=20&t=76088

Go to the bottom. The problem is already set up in an Excel sheet. They came to the same conclusion.

I ran it through Excel Solver and got the same thing using your info.

50% beef, 50% pork, at 75 cents a pound.