Weenies is a food processing plant which 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 ¼ pound of port product. All the other ingredients in the hot dogs and hot dog buns are in plentiful supply. Finally, the labor force at Weenies consists of 5 employees working full time (40 hours per week each). Each hot dog requires 3 minutes of labor, and each hot dog bun requires 2 minutes of labor. Each hot dog yields a profit of $0.40, and each bun yields a profit of $0.20. Weenies 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 the decisions, and the overall measure of performance for the decisions. B. Convert these descriptions of constraints and the measure of performance into quantitative expressions in terms of the data and decisions. C. Formulate a linear programming model and solve it. D. Formulate this same model algebraically. E. Use thre graphical method to solve this model.
Weenies is a food processing plant which 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 ¼ pound of port product. All the other ingredients in the hot dogs and hot dog buns are in plentiful supply. Finally, the labor force at Weenies consists of 5 employees working full time (40 hours per week each). Each hot dog requires 3 minutes of labor, and each hot dog bun requires 2 minutes of labor. Each hot dog yields a profit of $0.40, and each bun yields a profit of $0.20. Weenies 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 the decisions, and the overall measure of performance for the decisions.
B. Convert these descriptions of constraints and the measure of performance into quantitative expressions in terms of the data and decisions.
C. Formulate a linear programming model and solve it.
D. Formulate this same model algebraically.
E. Use thre graphical method to solve this model.
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