Question

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. What is objective function for the mathematical formulation, in words?

Answer 1

The objective function for determining the minimum cost way to blend beef and pork for Bill's Grill's hamburgers is the total cost function, which is calculated as 0.85x + 0.65y, where x and y represent the pounds of beef and pork respectively.

Step-by-step explanation:

To determine the minimum cost way to blend beef and pork to make hamburgers that have no more than 25% fat, we must establish an objective function which represents the total cost of mixing the two meats. The cost of beef is $0.85 per pound and pork is $0.65 per pound. Let's say we use x pounds of beef and y pounds of pork. The objective function would thus be the total cost, which is 0.85x + 0.65y. This function needs to be minimized subject to the constraint that the mixture should have no more than 25% fat.

It is important to note that the question provided seems to contain information related to a different economic concept regarding opportunity cost, as it discusses the trade-off between burgers and bus tickets for an individual named Alphonso. However, this does not directly pertain to the question about Bill's Grill and the objective function for mixing meats.