For Chapter 1, do a break-even analysis. For Chapter 2, 1. Formulate the stated problems as a linear model (clearly state decision variables, objective function, and constraints). ATTACH YOUR FORMULATIONS!!!!!!!!!!!!! 2. Find the optimal solution using graphical techniques as shown in class PowerPoint slides. 3. Find slack or surplus variables at each optimal solution. 4. Show all your work!

Chapter 1

1.

Pastureland Dairy makes cheese, which it sells at local supermarkets. The fixed monthly cost of production is $4,000, and the variable cost per pound of cheese is $0.21. The cheese sells for $0.75 per pound; however, the dairy is considering raising the price to $0.95 per pound. The dairy currently produces and sells 9,000 pounds of cheese per month, but if it raises its price per pound, sales will decrease to 5,700 pounds per month. Should the dairy raise the price?

Chapter 2

1.

A clothier makes coats and slacks. The two resources required are wool cloth and labor. The clothier has 150 square yards of wool and 200 hours of labor available. Each coat requires 3 square yards of wool and 10 hours of labor, whereas each pair of slacks requires 5 square yards of wool and 4 hours of labor. The profit for a coat is $50, and the profit for slacks is $40. The clothier wants to determine the number of coats and pairs of slacks to make so that profit will be maximized.

a. Formulate a linear programming model for this problem.

b. Solve this model by using graphical analysis.

2.

Universal Claims Processors processes insurance claims for large national insurance companies. Most claim processing is done by a large pool of computer operators, some of whom are permanent and some of whom are temporary. A permanent operator can process 16 claims per day, whereas a temporary operator can process 12 per day, and on average the company processes at least 450 claims each day, The company has 40 computer workstations. A permanent operator generates about 0.5 claims with errors each day, whereas a temporary operator average about 1.4 defective claims per day. The company wants to limit claims with errors to 25 per day. A permanent operator is paid $64 per day, and a temporary operator is paid $42 per day. The company wants to determine the number of permanent and temporary operators to hire to minimize costs.

a. Formulate a linear programming model for this problem.

b. Solve this model by using graphical analysis.