Chapter 1, Problem 59P

To determine

(a)

The choice between (1) returning the car with full tank (2) returning the car without filling it and pay $5.45/gallon (3) accept a fixed price of $50 for gas.

Answer to Problem 59P

For travelling 150 miles, the choice should be return the car with full gas tank.

Explanation of Solution

Given information:

• Car mileage − 28 miles per gallon
• Local price of gasoline − $3.95/gallon
• Travel miles − 150 miles
• Tank size of the car − 16 gallons

We will have to find the best alternative which will have very loss cost bearing. The cost from all three alternatives shall be evaluated.

Calculation

Considering the car gets 28 miles per gallon, to run 150 miles, the gallons of gas required will be:

$\text{NoG=}\frac{\text{Miles}}{\text{Mileage}}$

wherein: NoG − Number of Gallons

Miles − Miles to be covered

Mileage − Number of gallons required to cover one mile

$NoG=\frac{150}{28}=5.357$

So, to cover 150 miles 5.357 gallons of gas will be spent.

Let us now weigh all the three options:

1. Return the car with full tank:

In this case, the cost incurred will be as follows, depicted by C − Cost; NoG − Number of gallons and P − local price per gallon:

$\begin{array}{l}C=NoG\times P\\ C=5.357\times 3.95\\ C=\$21.16\end{array}$

2. Return the car without filling the gas tank:

In this case, the cost incurred will be calculated similar as the previous part but will be calculated at the price that the car company will be charging, that is, $5.45 per gallon

$\begin{array}{l}C=NoG\times P\\ C=5.357\times 5.45\\ C=\$29.20\end{array}$

3. Accept a fixed price:

Here we have to pay a fixed price of $50.00 to the rental company.

Conclusion:

Therefore, the best economical option for driving 150 miles is: (a) return the car with a full gastank.

To determine

(b)

The choice between (1) returning the car with full tank (2) returning the car without filling it and pay $5.45/gallon (3) accept a fixed price of $50 for gas.

Answer to Problem 59P

For travelling 300 miles, the choice should be return the car with full gas tank.

Explanation of Solution

Given information:

• Car mileage − 28 miles per gallon
• Local price of gasoline − $3.95/gallon
• Travel miles − 300 miles
• Tank size of the car − 16 gallons

We will have to find the best alternative which will have very loss cost bearing. The cost from all three alternatives shall be evaluated.

Calculation

Considering the car gets 28 miles per gallon, to run 300 miles, the gallons of gas required will be:

$NoG=\frac{Miles}{Mileage}$

wherein: NoG − Number of Gallons

Miles − Miles to be covered

Mileage − Number of gallons required to cover one mile

$NoG=\frac{300}{28}=10.714$

So, to cover 300 miles 10.714 gallons of gas will be spent.

Let us now weigh all the three options:

1. Return the car with full tank:

In this case, the cost incurred will be as follows, depicted by C − Cost; NoG − Number of gallons and P − local price per gallon:

$\begin{array}{l}C=NoG\times P\\ C=10.714\times 3.95\\ C=\$42.32\end{array}$

2. Return the car without filling the gas tank:

In this case, the cost incurred will be calculated similar as the previous part but will be calculated at the price that the car company will be charging, that is, $5.45 per gallon

$\begin{array}{l}C=NoG\times P\\ C=10.714\times 5.45\\ C=\$58.39\end{array}$

3. Accept a fixed price:

Here we have to pay a fixed price of $50.00 to the rental company.

Conclusion:

Therefore, the best economical option for driving 300 miles is: (a) return the car with a full gastank.

To determine

(c)

The choice between (1) returning the car with full tank (2) returning the car without filling it and pay $5.45/gallon (3) accept a fixed price of $50 for gas.

Answer to Problem 59P

For travelling 400 miles, the choice should be to pay the fixed price.

Explanation of Solution

Given information:

• Car mileage − 28 miles per gallon
• Local price of gasoline − $3.95/gallon
• Travel miles − 400 miles
• Tank size of the car − 16 gallons

We will have to find the best alternative which will have very loss cost bearing. The cost from all three alternatives shall be evaluated.

Calculation

Considering the car gets 28 miles per gallon, to run 400 miles, the gallons of gas required will be:

$\text{NoG=}\frac{\text{Miles}}{\text{Mileage}}$

wherein: NoG − Number of Gallons

Miles − Miles to be covered

Mileage − Number of gallons required to cover one mile

$NoG=\frac{400}{28}=14.29$

So, to cover 400 miles 14.29 gallons of gas will be spent.

Let us now weigh all the three options:

1. Return the car with full tank:

In this case, the cost incurred will be as follows, depicted by C − Cost; NoG − Number of gallons and P − local price per gallon:

$\begin{array}{l}C=NoG\times P\\ C=14.29\times 3.95\\ C=\$56.45\end{array}$

2. Return the car without filling the gas tank:

In this case, the cost incurred will be calculated similar as the previous part but will be calculated at the price that the car company will be charging, that is, $5.45 per gallon

$\begin{array}{l}C=NoG\times P\\ C=14.29\times 5.45\\ C=\$77.88\end{array}$

3. Accept a fixed price:

Here we have to pay a fixed price of $50.00 to the rental company.

Conclusion:

Therefore, the best economical option for driving 400 miles is: (c) pay fixed amount $50.

To determine

(d)

If the choice changes if there is a time worth $12/hr.

Answer to Problem 59P

The choice does not change if there is a time worth between $12/hr.

Explanation of Solution

Given information:

• Car mileage − 28 miles per gallon
• Local price of gasoline − $3.95/gallon
• Travel miles − 150 miles
• Tank size of the car − 16 gallons
• It takes 15minutes to fill the gas and the time is worth $12/hr

We will have to include the cost of time in the first option, while the remaining options do not change.

Calculation

• 150 miles
− Return the car with full tank:

In this case, the cost incurred will be as follows, depicted by C − Cost; NoG − Number of gallons and P − local price per gallon:

$\begin{array}{l}C=(NoG\times P)+CoT\\ C=5.357\times 3.95+(0.25\times 12)\\ C=21.16+3\\ C=\$24.16\end{array}$

• Return the car without filling the gas tank: $29.20
• Accept a fixed price: $50

Therefore, the best economical option for driving 150 miles is: (a) return the car with a full gastank.

• 300 miles
− Return the car with full tank:

In this case, the cost incurred will be as follows, depicted by C − Cost; NoG − Number of gallons and P − local price per gallon:

$\begin{array}{l}C=(NoG\times P)+CoT\\ C=10.714\times 3.95+(0.25\times 12)\\ C=42.32+\text{}3\\ C=45.32\end{array}$

• Return the car without filling the gas tank: $58.39
• Accept a fixed price: $50

Therefore, the best economical option for driving 300 miles is: (a) return the car with a full gastank.

• 400 miles
− Return the car with full tank:

In this case, the cost incurred will be as follows, depicted by C − Cost; NoG − Number of gallons and P − local price per gallon:

$\begin{array}{l}C=NoG\times P+\text{}CoT\\ C=14.29\times 3.95+(0.25\times 12)\\ C=56.45+\text{}3\\ C=\$59.45\end{array}$

• Return the car without filling the gas tank: $77.88
• Accept a fixed price: $50

Conclusion:

Therefore, the best economical option for driving 400 miles is: (c) pay fixed amount $50.