1. Use the graphical method to solve the following two problems (40 pts):

a). Maximize Z= 101 + 202, subject to -1 + 22 15 1+ 2 12 51 + 32 45 and 1 0, 2 0.

b). Maximize Z= 21 + 2, subject to 2 10 21 + 52 60 1 + 2 18 31 + 2 44 and 1 0, 2 0.

2. The WorldLight Company produces two light fixtures (products 1 and 2) that require both metal frame parts and electrical components. Management wants to determine how many units of each product to produce so as to maximize profit. For each unit of product 1, 1 unit of frame parts and 2 units of electrical components are required. For each unit of product 2, 3 units of frame parts and 2 units of electrical components are required. The company has 200 units of frame parts and 300 units of electrical components. Each unit of product 1 gives a profit of $1, and each unit of product 2, up to 60 units, gives a profit of $2. Any excess over 60 units of product 2 brings no profit, so such an excess has been ruled out.

(a) Formulate a linear programming model for this problem (20 pts).

(b) Use either the graphical method or EXCEL Solver to solve this model. What is the resulting total profit (10 pts)?

3. Weenies and Buns is a food processing plant which manufactures buns and frankfurters for hot dogs. 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 with Pigland, Inc., which specifies that a delivery of 800 pounds of pork product is delivered every Monday. Each frankfurter requires 1 4 pound of pork product. All the other ingredients in the buns and frankfurters 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 frankfurter requires 3 minutes of labor, and each bun requires 2 minutes of labor. Each frankfurter yields a profit of $0.88, and each bun yields a profit of $0.33. Weenies and Buns would like to know how many frankfurters and how many buns they should produce each week so as to achieve the highest possible profit.

(a) Formulate a linear programming model for this problem (20 pts).

(b) Use either the graphical method or EXCEL Solver to solve this model. What is the resulting total profit (10 pts)?