Chapter 5.S, Problem 8P

a)

Summary Introduction

To determine: The sensitivity to the problem in terms of the probability estimate of 0.35.

Introduction: Decision making is the procedure of selecting choices by identifying a decision, obtaining information and evaluating alternative resolutions. Always, step-by-step decision making process can help to make more deliberate, and thoughtful decisions in the organization. 

Answer to Problem 8P

The management should renew the motel rather than relocating.

Explanation of Solution

Given information:

It is given that the lease of theme part is about to expire. The management should decide whether to renew the lease for another 10 years or relocate the motel. The details about the two alternatives are as follows:

Options	Motel approved	Motel rejected
Renew	$500,000	$4,000,000
Relocate	$5,000,000	$100,000

Determine the sensitivity of the problem:

The graph shown below contains the range of values of probability of approved motel where the alternative is optimal:

If the value is low, renewal is best with the highest expected value.

If the value is high, relocate is best with the highest expected value

Slope of renew:

$\begin{array}{c}\text{Slope}=500,000-4,000,000\\ =-3,500,000\end{array}$

Equation for renew:

$4,000,000-3,500,000P$

Slope of relocate:

$\begin{array}{c}\text{Slope}=5,000,000-100,000\\ =4,900,000\end{array}$

Equation for renew:

$100,000+4,900,000P$

Determine the intersection between two lines:

It can be determined by equaling the equations of renew and relocate.

$\begin{array}{c}4,000,000-3,500,000P=100,00+4,900,000P\\ -3,500,000P-4,900,000P=100,000-4,000,000\\ -8,400,000P=-3,900,000\end{array}$

$\begin{array}{c}P=\frac{-3,900,000}{-8,400,000}\\ =0.4643\end{array}$

Optimal ranges are as follows:

Renew:

$P\left(\text{Approved}\right)=0\text{ to 0}\text{.4643}$

Relocate:

$P\left(\text{Approved}\right)=\text{0}\text{.4643 to 1}\text{.00}$

Conclusion

It is given that the percentage is 0.35 which is less than .4643. Hence, renew should be selected.

b)

Summary Introduction

To determine: The sensitivity to the problem in terms of the probability estimate of 0.45.

Introduction: Decision-making is the process that helps to make decision. It is the process of choosing a best alternative by evaluating many alternatives.

Answer to Problem 8P

The management should renew the motel rather than relocating.

Explanation of Solution

Given information:

It is given that the lease of theme part is about to expire. The management should decide whether to renew the lease for another 10 years or relocate the motel. The details about the two alternatives are as follows:

Options	Motel approved	Motel rejected
Renew	$500,000	$4,000,000
Relocate	$5,000,000	$100,000

Determine the sensitivity of the problem:

The graph shown below contains the range of values of probability of approved motel where the alternative is optimal:

If the value is low, renewal is best with the highest expected value.

If the value is high, relocate is best with the highest expected value

Slope of renew:

$\begin{array}{c}\text{Slope}=500,000-4,000,000\\ =-3,500,000\end{array}$

Equation for renew:

$4,000,000-3,500,000P$

Slope of relocate:

$\begin{array}{c}\text{Slope}=5,000,000-100,000\\ =4,900,000\end{array}$

Equation for renew:

$100,000+4,900,000P$

Determine the intersection between two lines:

It can be determined by equaling the equations of renew and relocate.

$\begin{array}{c}4,000,000-3,500,000P=100,00+4,900,000P\\ -3,500,000P-4,900,000P=100,000-4,000,000\\ -8,400,000P=-3,900,000\end{array}$

$\begin{array}{c}P=\frac{-3,900,000}{-8,400,000}\\ =0.4643\end{array}$

Optimal ranges are as follows:

Renew:

$P\left(\text{Approved}\right)=0\text{ to 0}\text{.4643}$

Relocate:

$P\left(\text{Approved}\right)=\text{0}\text{.4643 to 1}\text{.00}$

Conclusion

Conclusion: It is given that the percentage is 0.45 which is less than .4643. Hence, renew should be selected.

c)

Summary Introduction

To determine: The range of payoff for renew reject for the selected alternative.

Introduction: Decision-making is the process that helps to make decision. It is the process of choosing a best alternative by evaluating many alternatives.

Answer to Problem 8P

The management should renew the motel rather than relocating.

Explanation of Solution

Given information:

It is given that the lease of theme part is about to expire. The management should decide whether to renew the lease for another 10 years or relocate the motel. The details about the two alternatives are as follows:

Options	Motel approved	Motel rejected
Renew	$500,000	$4,000,000
Relocate	$5,000,000	$100,000

The estimated payoff except for $4 million and the probability of approval is 0.35.

Determine the payoff:

Renew:

$\text{Renew}=0.35\left(500,000\right)+0.65\left(4,000,000\right)$

X should be plugged in instead of 4,000,000 in the above equation

$\text{Renew}=0.35\left(500,000\right)+0.65x$

Relocate:

$\begin{array}{c}\text{Relocate}=0.35\left(5,000,000\right)+0.65\left(100,000\right)\\ =1,750,000+65,000\\ =1,815,000\end{array}$

Equal the equations of renew and relocate to solve x:

Equations of renew and relocate should be equaled to determine the value of x.

$\begin{array}{c}0.35\left(500,000\right)+0.65x=\$1,815,000\\ 175,000+0.65x=\$1,815,000\\ 0.65x=\$1,815,000-175,000\end{array}$

$\begin{array}{c}0.65x=1,640,000\\ x=\frac{1,640,000}{0.65}\\ =2,523,077\end{array}$

The original decisions at payoff is $4,000,000 should be decreased to $2,523,077 for the decision to change from renew to relocate.

Conclusion

When x is $2,523,077, there would be indifference between renew and relocate.

When x is less than $2,523,077, the decision would be changed to relocate.