Use This Information to Answer the Following Questions -Use the Sensitivity Report to Answer the Following Questions:
A

question 18

Essay

Use this information to answer the following questions.
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.

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.
$\begin{array}{ccccccc}\hline \text { Cell } & \text { Name } & \begin{array}{c}\text { Final } \\\text { Value }\end{array} & \begin{array}{c}\text { Reduced } \\\text { Cost }\end{array} & \begin{array}{c}\text { Objective } \\\text { Coefficient }\end{array} & \begin{array}{c}\text { Allowable } \\\text { Increase }\end{array} & \begin{array}{c}\text { Allowable } \\\text { Decrease }\end{array} \\\hline \text { SC\$13 } & \text { A1 } & 5 & 0 & 2 & 1 & 1 \mathrm{E}+30 \\\hline \text { SD\$13 } & \text { A2 } & 0 & 1 & 3 & 1 \mathrm{E}+30 & 1 \\\hline\text { SE\$13 } & \text { A3 } & 0 & 1 & 2 & 1 \mathrm{E}+30 & 1 \\\hline \text { SF\$13 } & \text { A4 } & 0 & 3 & 4 & 1 \mathrm{E}+30 & 3 \\\hline \text { SC\$14 } & \text { B1 } & 0 & 2 & 4 & 1 \mathrm{E}+30 & 2 \\\hline\text { SD\$14 } & \text { B2 } & 0 & 3 & 5 & 1 \mathrm{E}+30 & 3 \\\hline \text { SE\$14 } & \text { B3 } & 0 & 2 & 3 & 1 \mathrm{E}+30 & 2 \\\hline \text { SF\$14 } & \text { B4 } & 3 & 0 & 1 & 3 & 1 \mathrm{E}+30 \\\hline\text { SC\$15 } & \text { C1 } & 0 & 1 & 3 & 1 \mathrm{E}+30 & 1 \\\hline\text { SD\$15 } & \text { C2 } & 4 & 0 & 2 & 1 & 1 \mathrm{E}+30 \\\hline\text { SE\$15 } & \text { C3 } & 2 & 0 & 1 & 1 & 1 \mathrm{E}+30 \\\hline\text { SF\$15 } & \text { C4 } & 0 & 4 & 5 & 1 \mathrm{E}+30 & 4 \\\hline\end{array}$

$$\begin{array}{l}\text { Constraints }\\\begin{array} { l l c c c c c } \hline \text { Cell } & \text { Name } & \begin{array} { c } \text { Final } \\\text { Value }\end{array} & \begin{array} { c } \text { Shadow } \\\text { Price }\end{array} & \begin{array} { c } \text { Constraint } \\\text { R.H. Side }\end{array} & \begin{array} { c } \text { Allowable } \\\text { Increase }\end{array} & \begin{array} { c } \text { Allowable } \\\text { Decrease }\end{array} \\\hline \text { \$G\$13 } & \text { A constraint } & 10 & 0 & 40 & 1 \mathrm { E } + 30 & 30 \\\hline \text { \$G\$14 } & \text { B constraint } & 3 & 0 & 40 & 1 \mathrm { E } + 30 & 37 \\\hline \text { \$G\$15 } & \text { C constraint } & 10 & 0 & 40 & 1 \mathrm { E } + 30 & 30 \\\hline \text { \$C\$16 } & \text { Claim Type 1 } & 5 & 2 & 5 & 15 & 5 \\\hline \text { \$D\$16 } & \text { Claim Type 2 } & 4 & 2 & 4 & 15 & 4 \\\hline \text { \$E\$16 } & \text { Claim Type 3 } & 2 & 1 & 2 & 30 & 2 \\\hline \text { \$F\$16 } & \text { Claim Type 4 } & 3 & 1 & 3 & 37 & 3 \\\hline\end{array}\end{array}$$
-Use the Sensitivity Report to answer the following questions:
a.Suppose that the number of type 1 claims increases to 6 and the number of type 2 claims decreases to 3.What impact would this simultaneous change have on the current optimal objective function value?
b.What is the impact on the current solution and the objective function value if secretary A takes 3 hours to process claim 1 and secretary B takes 5 hours to process claim 1?

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Definitions:

Regression Analysis

A statistical method for examining the relationship between a dependent variable and one or more independent variables.

Index

A method or system for ordering or categorizing objects or data, often used in reference to databases, stock markets, or economic indicators.

Strength Of Association

A measure indicating the relationship's intensity between two variables, showing how closely the variables are related.

Variables

Elements or characteristics within a study that can vary and have different values among subjects.