Bills Burgers is a popular restaurant that is famous for its hamburgers. The res

Question

Bills Burgers is a popular restaurant that is famous for its hamburgers. The restaurant mixes fresh ground beef (B) and pork (P) with a secret ingredient to make delicious quarter-pound hamburgers that are advertised as having no more than 25% fat. The restaurant can buy beef (B) containing 80% meat and 20% fat at $0.85 per pound. He can buy pork (P) containing 70% meat and 30% fat at $0.65 per pound. Bills wants to determine the minimum cost way to blend the beef (B) and pork (P) 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 (B) and the percentage of pork (P) to combine.) b. Sketch the feasible region for this problem. Label all axes, constraints, extreme point(s) and the feasible region. (8 pts) c. Indicate the optimal objective function value at the extreme point. d. Briefly indicate why it may not be feasible or efficient to enumerate extreme points to find an optimal solution to a linear programming problem.

Explanation / Answer

the equation is that we have to minimize

0.85x + .75y such that x + y = 1, x >=0, y >=0, and .2x + .3y < = .25

Now if we plot the graph for all the equation.

we will see that the optimal solution is when x=0.5 and y=0.5. So basically we need to fix beep and pork in the ratio of 1:1 to get the proper meat for burger.

It will cost $0.8 per pound.

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