Question #1. 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 claim with errors each day, whereas a temporary operator averages 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. c. Explain the effect on the optimal solution of changing the daily pay for a permanent claims processor from $64 to $54. d. Explain the effect of changing the daily pay for a temporary claims processor from $42 to $36. e. What would be the effect on the optimal solution if Universal Claims Processors decided not to try to limit the number of defective claims each day? f. Explain the effect on the optimal solution if the minimum number of claims the firm processes each day increased from 450 to at least 650.

Question #3 The Brintons live on a farm in South Georgia on which they produce a variety of crops and livestock, including pecans. It has 5 acres of pecan trees that yield approximately 1,000 pounds of unshelled pecans per acre each year. The family uses all of its pecan harvest to produce pecan pies, cookies, 1-pound bags of shelled pecans, and 5-pound bags of unshelled pecans, which it sells in town at the local farmers' market. The family sells pies for $5, packages of a dozen cookies for $3, bags of shelled pecans for $7, and bags of unshelled pecans for $16. A shelled pecan is half the weight of an unshelled pecan. It requires 4 ounces of shelled pecans to make a pie, and 6 ounces of shelled pecans to make a dozen cookies. The pies and cookies are baked in the family oven, and there are 120 hours of baking time available. It takes 55 minutes to bake a batch of 4 pies and 15 minutes to bake a batch of 2 dozen cookies. It requires family members 6 minutes to shell the pecans for a pie and package it, 4 minutes to shell the pecans for cookies and to package them, 10 minutes to shell the pecans for a 1-pound bag of shelled pecans and package them, and 1 minute to package a bag of unshelled pecans; and there are 300 hours available from family members for shelling and packaging. The Brintons want to know how many pecan pies, dozens of cookies, and bags of shelled and unshelled pecans to produce to maximize its sales revenues. a. Formulate a linear programming model for this problem. b. Solve the linear programming model formulated in (a.) for the Brinton farm using the computer. c. Are there any extra (slack) resources available? d. If the Brinton family could obtain additional resources, which one would be of most value to them? How much would they be willing to pay for this resource? Why? e. If the family could obtain an additional 500 pounds of pecans or 30 hours of oven time, which should they choose? f. The family is thinking about buying a bigger oven for $3,000. If they do so, they could make a batch of 5 pies or a batch of 3 dozen cookies at one time. Should they buy the oven? Explain your answer.