Chapter 1.1, Problem 95E

a.

To determine

Find the linear equation giving the total cost C of operating the bulldozer for thours.(Include the purchase cost of the bulldozer)

Answer to Problem 95E

The linear equation for the given question will be $C=30.75t+36500$ .

Explanation of Solution

Given: It is given in the question that a contractor purchases a bulldozer for $\$36500$ .The bulldozer requires an average expenditure of $\$11.25$ per hour for fuel and maintenance ,and the operator is paid $\$19.50$ per hour.

Concept Used:

In this, use the concept of understanding the right variable and constant to make a linear equation .

Calculation: Let the linear equation is of the form of $C=at+b$ .

initial Cost for the purchase a bulldozer ,b = $\$36500$

Now, the Extra cost (fuel + operator) = $\$(11.25+19.50)$

If the extra cost be at the time thours ,then $\$(11.25+19.50)\times t$

Therefore, Total cost C = Initial cost + Extra cost for t hours

  $\begin{array}{l}=36500+(11.25+19.50)\times t\\ =36500+30.75\times t\\ =30.75t+36500\end{array}$

So, the equation be $C=30.75t+36500$ .

Conclusion:

The equation be $C=30.75t+36500$ .

b.

To determine

Find the equation for the revenue R derived from t hours of use.

Answer to Problem 95E

The equation for the revenue R be $R=\$80t$ .

Explanation of Solution

Given:

It is given in the question that the customers has charged $\$80$ per hour of bulldozer use.

Concept Used:

In this, use the concept of understanding the right variable and constant to make a linear equation and use the formula $\mathrm{Re}venue=Rate\times timeused$ .

Calculation: In this, the amount that charged from the customer per hour = $\$80$

The time at which the bulldozer be used to work = t hours

So, $\mathrm{Re}venue=Rate\times timeused$

  $\begin{array}{l}=80(\$/hr)\times t(hr)\\ =\$80t\end{array}$

The equation is $R=\$80t$

Conclusion:

The equation is $R=\$80t$

c.

To determine

Find the equation for the profit gained from t hours of use .

Answer to Problem 95E

The equation for the profit gained from t hours of use is $P=49.25t-36500$ .

Explanation of Solution

Given: It is given in the question that a contractor purchases a bulldozer for $\$36500$ .The bulldozer requires an average expenditure of $\$11.25$ per hour for fuel and maintenance ,and the operator is paid $\$19.50$ per hour.

Concept Used:

In this, use the concept of understanding the right variable and constant to make a linear equation and use the formula $(P=R-C)$

Calculation: In this ,the revenue got from part (b) , $R=\$80t$

The cost that got from part (a) , $C=30.75t+36500$

So,by using the formula $(P=R-C)$ ,profit will be get it.

  $\begin{array}{l}\mathrm{Pr}ofit=\mathrm{Re}venue-Cost\\ P=80t-(30.75t+36500)\\ P=80t-30.75t-36500\\ P=49.25t-36500\end{array}$

So ,the equation of Profit is, $P=49.25t-36500$ .

Conclusion:

The equation of Profit is, $P=49.25t-36500$ .

d.

To determine

Find the break − even point (the number of hours the bulldozer must be used to gain a profit of $0$ dollars) by using the result in part (c).

Answer to Problem 95E

The break down even point is , $t=741.11h$ .

Explanation of Solution

Given:

It is given in the question that the equation obtained in part (c) is $P=49.25t-36500$ .

Concept Used:

In this, use the concept of understanding the right variable and constant to make a linear equation and use the formulaCalculation: To find the break down ,such that the number of hours the bulldozer must be used to gain a profit of $0$ dollars, so put $P=0$ in the equation.

  $\begin{array}{l}P=49.25t-36500\\ 0=49.25t-36500\\ 36500=49.25t\\ 49.25t=36500\\ t=\frac{36500}{49.25}\\ t=741.11h\end{array}$

The time for the break down is, $t=741.11h$ .

Conclusion:

The time for the break down is, $t=741.11h$ .