Sоlve this lineаr prоgrаmming prоblem using the grаphical method. You may use scratch paper to construct your graph and complete your calculations. (You will upload your graph and calculations after completing the exam.) The Village Butcher Shop traditionally makes its meat loaf from a combination of lean ground beef and ground pork. The ground beef contains 80% meat and 20% fat and costs the shop $ 5 per pound, while the ground pork contains 60% meat and 40% fat and costs $3 per pound. The shop wants to minimize its cost while meeting the following requirements: Fat content of the mixture must not exceed 30%. At least 40% of the mixture must be ground pork. Meat content must be at least 50% of the total mixture. No more than 60% of the mixture can be ground beef. Total weight of the mixture must be 50 pounds. How much of each kind of meat should the shop use in each pound of meat loaf? Solve this LP with the graphical method. In the box below, answer all of the following: Define the decision variables. Write the objective function. Write all constraints for the problem. List the coordinates of all extreme points of the feasible region. Identify the extreme point or points that produce the optimal value. State how many pounds of ground beef and ground pork should be used in the 50-pound mixture. Report the minimum total cost. Show the objective-function value at each extreme point or otherwise explain how you identified the optimum.
Fоrmulаte аn LP mоdel thаt maximizes prоfit. Do not solve the model. THIRDsty produces three types of canned juice drinks (A, B and C) using fresh strawberry, grape and apple juice. The daily supply is limited to 3000 lb of strawberry juice, 1200 lb of grape juice and 1500 lb of apple juice. The cost per lb is $2 per lb of strawberry juice, $1 per lb of grape juice and $0.9 per lb of apple juice. Drink A must have at least 20% strawberry juice and at most 35% apple juice. Drink B must have at least 25% strawberry juice and at least 25% grape juice. Drink C must have at most 40% grape juice. All drinks are sold in 1 lb cans. The price per can is $1.15, $1.25 and $1.20 for drinks A, B, and C. Formulate an LP to maximize the profit. Your answer must clearly include: definitions of all decision variables, total revenue, total ingredient cost, the profit-maximization objective, supply constraints, all drink-composition constraints, non-negativity restrictions.