SOLUTION: PROBLEM 3: (13 marks) An insurance company has three secretaries, A, B, and C that each is capable of processing four different types of insurance claims. The amount of time requir
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Question 1150940: PROBLEM 3: (13 marks) An insurance company has three secretaries, A, B, and C that each is capable of processing four different types of insurance claims. The amount of time required by each secretary to process a particular type of a claim is summarized in the following table Processing Time in Hours Claim Type 3 2 2 4 4 1 5 Secretary В 4 2 3 1 On a typical week, the insurance firm has 5 type 1 claims, 4 type 2 claims, 2 type 3 claims, and 3 type 4 claims. Each secretary works a maximum of 40 hours per week. The office manager wants to know how many of each type of an insurance claim should be processed by each secretary to minimize the total processing time Sensitivity Report Adjustable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease SC$13 A1 5 2 1E+30 1E+30 1E+30 $D$13 A2 0 1 1 $E$13 $F$13 SC$14 $D$14 SE$14 $F$14 $C$15 $D$15 $E$15 $F$15 A3 0 2 1 A4 0 4 1E+30 B1 2 1E+30 2 B2 0 3 1E+30 3 1E+30 2 B3 0 2 B4 3 0 1 3 1E+30 C1 0 1 1E+30 C2 4 2 1E+30 2 1E+30 C3 0 C4 0 5 1E+30 4 Constraints Allowable Allowable Final Shadow Constraint Cell $G$13 A constraint $G$14 B constraint Name Value Price R.H. Side Increase Decrease 1E+30 1E+30 1E+30 15 10 40 30 3 10 5 0 0 40 37 30 5 $G$15 C constraint $C$16 Claim Type 1 $D$16 Claim Type 2 $E$16 Claim Type 3 $F$16 40 5 4 2 4 4 2 2 2 30 Claim Type 4 3 37 OONGN BC Use the Sensitivity Report to answer the following questions A) What is the total minimal processing time in hours? (1 mark) B) Suppose that secretary A can process a type 2 claim in two hours rather than three hours How would this impact the current optimal solution? (1 mark) C) Assume that secretary C can process a type 4 claim in 6 hours rather than 5 hours. How would this impact the current optimal solution? (1 mark) D) Currently, secretary C is not processing any type 4 claims. Suppose that we force secretary C to process one type 4 claim. What impact would this have on the optimal solution? (2 mark) E) Which constraints are binding? (2 mark) F) Suppose that secretary A has a total of 45 weekly hours. What impact would this have on the current optimal solution? (2 mark) G) What is the total number of unused weekly hours for secretary B? (2 marks) H) Suppose that the number of type 4 claims increases to 4. What impact would this have on the current bptimal solution? (2 marks)
