Chapter 1.3, Problem 99E

a .

To determine

To write: the linear equation giving the total cost C of operating the equipment for t hours.

Answer to Problem 99E

  $C=21t+42000$

Explanation of Solution

Given:

Cost of delivery truck is $42,000.

Average expenditure on fuel and maintenance is $9.50 per hour.

Operator is paid $11.50 per hour.

Total cost C of operating the equipment for t hours is:

C = cost of delivery truck + cost of fuel and maintenance + cost of operator

  $\begin{array}{c}C=42,000+\left(9.50\right)t+\left(11.50\right)t\\ =42,000+9.50t+11.50t\\ =42,000+21t\end{array}$

b.

To determine

To write:the equation for the revenue R obtained from t hours of use.

Answer to Problem 99E

  $R=45t$

Explanation of Solution

Given:

Customers are charged $45 per hour of machine use.

Revenue = Hourly rate $\times$ Number of hours

Since machine is used for t hours at the rate $45 per hour. So, revenue function is given by:

  $\begin{array}{c}R=45\times t\\ =45t\end{array}$

c.

To determine

To find: the equation for the profit obtained from t hours of use.

Answer to Problem 99E

  $P=24t-42,000$

Explanation of Solution

From part (a), the cost function is given by $C=21t+42000$ .

From part (b), the revenue function is given by $R=45t$ .

Now, it is known that,

Profit = Revenue − Cost

  $\begin{array}{c}P=R-C\\ =45t-\left(21t+42,000\right)\\ =45t-21t-42,000\\ =24t-42,000\end{array}$

d.

To determine

To find: the break-even point.

Answer to Problem 99E

  $t=1,750\text{ hours}$

Explanation of Solution

Break-even point is the number of hours for which the machine should be operated to yield $0 profit.

So, the objective is to find t for which $P=0$ .

Consider,

  $\begin{array}{c}P=0\\ 24t-42,000=0\\ 24t=42,000\\ t=1,750\end{array}$

Thus, the equipment should be used for 1,750 hours to be break-even, that is to obtian $0 profit.