1. (20\%) The Good OR is a food processing plant which manufactures hot dogs and buns. They grind their own flour for the buns at a maximum rate of 200 pounds per week. Each bun requires 0.1 pound of flour. They currently have a contract which specifies that a delivery of 800 pounds of pork. Each hot dog requires 1/4 pound of pork. Finally, the labor force at the Good OR consists of 5 employees working full time (40 hours per week each). Each hot dog requires 3 minutes of labor, and each bun requires 2 minutes of labor. Each hot dog yields a profit of $2, and each bun yields a profit of $1. The Good OR would like to know how many hot dogs and how many buns they should produce each week so as to achieve the highest possible profit. (a) Formulate a linear programing model for this problem. (5\%) (b) Use the Simplex method step by step to solve this model for one iteration. (10\%) (c) Suppose the optimal solution is producing 3200 hot dogs and 1200 buns. What are the defining equations of the optimal solution (5%). 1. (20\%) The Good OR is a food processing plant which manufactures hot dogs and buns. They grind their own flour for the buns at a maximum rate of 200 pounds per week. Each bun requires 0.1 pound of flour. They currently have a contract which specifies that a delivery of 800 pounds of pork. Each hot dog requires 1/4 pound of pork. Finally, the labor force at the Good OR consists of 5 employees working full time (40 hours per week each). Each hot dog requires 3 minutes of labor, and each bun requires 2 minutes of labor. Each hot dog yields a profit of $2, and each bun yields a profit of $1. The Good OR would like to know how many hot dogs and how many buns they should produce each week so as to achieve the highest possible profit. (a) Formulate a linear programing model for this problem. (5\%) (b) Use the Simplex method step by step to solve this model for one iteration. (10\%) (c) Suppose the optimal solution is producing 3200 hot dogs and 1200 buns. What are the defining equations of the optimal solution (5%)