1. Our company Manufacturing makes two types of rocking chairs specifically designed for men and women known as the His and hers models. Each chair requires four legs and two rockers but differing number of wooden dowels. Each His chair requires four short dowels and eight long dowels while each hers chair requires eight short dowels and four long dowels. Each His chair contributes $10 in profit while each hers chair contributes $12. The company has 900 legs, 400 rockers, 1,200 short dowels, and 1,056 long dowels available. The company wants to maximize its profit while also ensuring that it makes at least half as many His chairs as hers chairs.
a. Formulate an LP model for this problem.
b. Sketch the feasibility region for this problem.
c. Find the optimal solution graphically and using the Solver.
2. B-girl is a popular college restaurant that is famous for its hamburgers. The owner of the restaurant , Bill, mixes fresh ground beef and pork with 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 represent the percentage of beef and percentage of pork to combine.)
b. Sketch the feasible region.
c. Determine the optimal solution using Solver.
3. A Bank has $650.00 in assets to allocate among investments in bonds, home mortgages, car loans, and personal loans. Bonds are expected to produce a return of 10%, mortgages 8.5%, car loans 9.5%, and personal loans 12.5%. To make sure the portfolio is not too risky, the bank wants to restrict personal loans to no more than the 25% of the total portfolio. The bank also wants to ensure that more money is invested in mortgages than personal loans. The bank also wants to invest more in bonds than personal loans.
a. Formulate an LP model for this problem with the objective of maximizing the expected return on the portfolio.
b. Implement your model in a spreadsheet and solve it.
c. What is the optimal solution?
4. The graph below represents various flows that can occur through a sewage treatment plant with the numbers on the arc representing the maximum flow (in tons of sewage per hour) that can be accommodated. Formulate an LP model to determine the maximum tons of sewage per hour that can be produced by this plant.