Weenies and Buns is a food processing plant that manufactures hot dogs and hot dog buns. They grind their own flour for the hot dog buns at a maximum rate of 200 pounds per week. Each hot dog bun requires 0.1 pound of flour. They currently have a contract with Pigland, Inc., which specifies that a delivery of 800 pounds of pork product is delivered every Monday. Each hot dog requires 1/4 pound of pork product. All the other ingredients in the hot dogs and hot dog buns are in plentiful supply. Finally, the labor force at Weenies and Buns consists of five employees working full time (40 hours per week each). Each hot dog requires three minutes of labor, and each hot dog bun requires two minutes of labor. Each hot dog yields a profit of $0.20, and each bun yields a profit of $0.10.
Weenies and Buns would like to know how many hot dogs and how many hot dog buns they should produce each week so as to achieve the highest possible profit.
a. Identify verbally the decisions to be made, the constraints on these decisions, and the overall measure of performance for the decisions.
b. Convert these verbal descriptions of the constraints and the measure of performance into quantitative expressions in terms of the data and decisions.
c. Formulate and solve a linear programming model for this problem on a spreadsheet.
d. Formulate this same model algebraically.
e. Use the graphical method to solve this model. Decide yourself whether you would prefer to do this by hand or by using the Graphical Linear Programming and Sensitivity Analysis module in your Interactive Management Science Modules?
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