#9
Assignment #5
More Linear Programming Models
(solve with STORM and analyze)
15 points
Due: September 28
Part I
The manager of the McDoodle franchise wants to determine how many sausage biscuits and ham biscuits to prepare each morning for breakfast customers. Each type of biscuit requires the following resources
Bisquit .. Labor(hr) .. Sausage(lb) .. Ham(lb) .. Flour(lb)
Sausage .. 0.010 .......... 0.10 ............. ---- ............ 0.04 Ham ...... 0.024 ........... ---- .............. 0.15 ............ 0.04
The franchise has 6 hours of labor available each morning. The manager has a contract with a local grocer for 30 pounds of sausage and 30 pounds of ham each morning. The manager also purchases 16 pounds of flour. The profit for a sausage bisquit is $0.60; the profit for a ham biscuit is $0.50. The manager wants to know the number of each type of biscuit to prepare each morning in order to maximize profit.
a) Define the linear programming model.
b) Solve the model using STORM.
c) Analyze the STORM printout for the manager.
d) How much extra sausage and ham are left over at the optimal solution point? Is there any idle labor time? Explain these values to the manager.
e) Identify the shadow prices for each of the resource constraints. Explain to the manager what these values mean.
f) Explain to the manager which resource constrains profit the most.
Part II
The McCoy family owns 410 acres of farmland in North Carolina on which they grow corn and tobacco. Each acre of corn costs $105 to plant, cultivate, and harvest; each acre of tobacco costs $210. The McCoys have a budget of $52,500 for next year. The government limits the number of acres of tobacco that can be planted to 100. The profit from each acre of corn is $300; the profit from each acre of tobacco is $520. The McCoys want to maximize their profit.
a) Define the linear programming model.
b) Solve the model using STORM.
c) Analyze the STORM printout for the McCoys.
d) The McCoys have an opportunity to lease some extra land from a neighbor. The neighbor is offering the land to them for $110 per acre. Should the McCoys lease the land at that price? What is the maximum price the McCoys should pay their neighbor for the land, and how much should they lease at that price? Explain your answer to the McCoys.
e) The McCoys are considering taking out a loan to increase their budget. For each dollar they borrow, how much additional profit would they make? If they borrowed an additional $1,000, would the number of acres of corn and tobacco they plant change? Explain your answer to the McCoys.
NOTE:
For each of these problems, you must turn in the following in order:
- linear programming model
- STORM printout
- Report (to manager of McDoodles (part I) or to McCoys (part II)) -- This report must be written in a professional manner, include the problem definition, and be descriptive and complete.
- supporting calculations