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:

Flexed

Bent or tensed, often referring to a muscle position.

Fibula

A long, thin bone located on the lateral side of the tibia in the lower leg, important for stabilizing the ankle and supporting muscles.

Ulna

A bone in the forearm that runs from the elbow to the smallest finger, and when in anatomical position, it is found on the medial side of the forearm.

Tibia

The shinbone or larger and stronger of the two bones in the lower leg, extending from the knee to the ankle.