How to Minimize Total Cost for Making Meat Loaf at Julio's Meat Market?
What is the optimal combination of ground beef and ground pork to minimize the total cost of making meat loaf at Julio's Meat Market?
Solution to Minimize Total Cost
Steps to Find Optimal Combination:
First, we need to determine the total weight of the meat loaf that needs to be mixed. The lean meat should be at least 45 pounds based on the 70% lean requirement.
Next, we set up the optimization problem:
Minimize: 0.95x + 0.65y
Subject to:
x + y ≥ 50 (using at least 50 pounds of ground pork)
x + y ≤ 490 (using at most 490 pounds of ground beef)
0.7x + 0.3y ≥ 45 (meeting the 70% lean requirement)
By solving the equations, we find that the optimal combination is 1.76 pounds of ground beef and 0.9 pounds of ground pork.
Total Cost Calculation:
The total cost is: 0.95(1.76) + 0.65(0.9) = $0.97 per pound
Therefore, to minimize the total cost while meeting the requirements, Julio's Meat Market should mix 1.76 pounds of ground beef and 0.9 pounds of ground pork for making meat loaf.