Chapter 1, Problem 59P

a).

To determine

To choose:An option from the given options.

Answer to Problem 59P

The driver will choose the option (1) return the car with full tank.

Explanation of Solution

The driver has three options to pick given that local price is $3.5 per gallon and the car has a mileage of 25 miles per gallon and the capacity of the tank is 16 gallons and Stopping at filling station takes 20 minutes and the worth of time is $15 per hour.

The following options are as follows:

(1) return the car with full gas tank,

(2) return it without filling it and pay $5.75 per gallon or

(3) accept a fixed price of $60 for gas.

When the driver drives 150 miles.

The gas consumed and cost to filling the emptied tank is calculated as follows:

  $\begin{array}{c}GasConsumed=\frac{150}{25}\\ =6gallons\end{array}$

  $\begin{array}{c}\mathrm{Cos}toffilling\tan k=6\times 3.5\\ =\$21\end{array}$

Therefore, the driver will choose to return the car with a full tank as the cost of filling the emptied tank is less than the fixed cost of $60.

b).

To determine

To choose:An option from the given options.

Answer to Problem 59P

The driver will choose option (1) return car with full tank.

Explanation of Solution

The driver has three options to pick given that local price is $3.5 per gallon and the car has a mileage of 25 miles per gallon and the capacity of the tank is 16 gallons and Stopping at filling station takes 20 minutes and the worth of time is $15 per hour.

The following options are as follows:

(1) return the car with full gas tank,

(2) return it without filling it and pay $5.75 per gallon or

(3) accept a fixed price of $60 for gas.

When the driver drives 300 miles.

The gas consumed and cost to filling the emptied tank is calculated as follows:

  $\begin{array}{c}GasConsumed=\frac{300}{25}\\ =12gallons\\ \mathrm{Cos}toffilling\tan k=12\times 3.5\\ =\$42\end{array}$

Therefore, the driver will choose to return the car with a full tank as the cost of filling the emptied tank is less than the fixed cost of $60.

c).

To determine

To choose:An option from the given options.

Answer to Problem 59P

The driver will choose option (3) accept a fixed price of $60 for gas.

Explanation of Solution

The driver has three options to pick given that local price is $3.5 per gallon and the car has a mileage of 25 miles per gallon and the capacity of the tank is 16 gallons and Stopping at filling station takes 20 minutes and the worth of time is $15 per hour.

The following options are as follows:

(1) return the car with full gas tank,

(2) return it without filling it and pay $5.75 per gallon or

(3) accept a fixed price of $60 for gas.

When the driver drives 450 miles.

The gas consumed and cost to filling the emptied tank is calculated as follows:

  $\begin{array}{c}GasConsumed=\frac{450}{25}\\ =18gallons\\ \mathrm{Cos}toffilling\tan k=18\times 3.5\\ =\$63\end{array}$

Therefore, the driver will choose to accept a fixed cost of $60 as this is less than the cost of filling the tank.

d).

To determine

To choose:An option from the given options.

Explanation of Solution

The driver has three options to pick given that local price is $3.5 per gallon and the car has a mileage of 25 miles per gallon and the capacity of the tank is 16 gallons and Stopping at filling station takes 20 minutes and the worth of time is $15 per hour.

The following options are as follows:

(1) return the car with full gas tank,

(2) return it without filling it and pay $5.75 per gallon or

(3) accept a fixed price of $60 for gas.

When stopping at filling station takes 20 minutes and the worth of time is $15 per hour how it will affect the decision of driver.

The cost of stopping at the gas station is calculated as follows:

  $\begin{array}{c}\mathrm{Cos}tofstoppingatgasstation=15\times \frac{20}{60}\\ =\$5\end{array}$

Part (a) When the driver drives 150 miles.

The gas consumed and cost to filling the emptied tank is calculated as follows:

  $\begin{array}{c}GasConsumed=\frac{150}{25}\\ =6gallons\\ \mathrm{Cos}toffilling\tan k=6\times 3.5+5\\ =\$21+5\\ =\$26\end{array}$

Even after considering the cost of stopping at gas station driver will choose option (1) return with a full tank.

Part (b) When the driver drives 300 miles.

The gas consumed and cost to filling the emptied tank is calculated as follows: $\begin{array}{c}GasConsumed=\frac{300}{25}\\ =12gallons\\ \mathrm{Cos}toffilling\tan k=12\times 3.5+5\\ =\$42+5\\ =\$47\end{array}$

Even after considering the cost of stopping at gas station driver will choose option (1) return with a full tank.

Part (c)When the driver drives 450 miles.

The gas consumed and cost to filling the emptied tank is calculated as follows:

  $\begin{array}{c}GasConsumed=\frac{450}{25}\\ =18gallons\\ \mathrm{Cos}toffilling\tan k=18\times 3.5+5\\ =\$63+5\\ =\$68\end{array}$

Therefore, the driver will choose to accept a fixed cost of $60 as this is less than the cost of filling the tank.

Economics Concept Introduction

Opportunity Cost: It is the cost of the next best alternative forgone while doing an action.