Chapter 3.1, Problem 48AYU

(a)

To determine

To find: the new bicycle daily fixed cost if the manufacturer is open for business 20days per month.

Answer to Problem 48AYU

The new daily fixed costs are $\$1805$ .

Explanation of Solution

Given:

The cost function as $C=90x+1800$ , which is the cost of manufacturing x bicycles in a day.

Now, the rent has been increased to $100 per month.

Calculation:

Since the business is open for 20 days in a month, the new additional cost would be given by

  $\$\frac{100}{20}$

Hence the new daily fixed costs are

  $\begin{array}{l}\$\left(1800+\frac{100}{20}\right)\hfill \\ \begin{array}{l}=\$\left(1800+5\right)\\ =\$1805\end{array}\hfill \\ \hfill \end{array}$

Conclusion:

Therefore, the new daily fixed costs are $\$1805$ .

(b)

To determine

To write: a linear model that expresses the cost C of manufacturing x bicycles in a day with the higher rent.

Answer to Problem 48AYU

The linear model expressing the cost is as follows $C=90x+1805$ .

Explanation of Solution

Calculation:

  $\begin{array}{l}m=90dollars\hfill \\ b=1805dollars\hfill \end{array}$

The slope is still 90 dollars because the variable cost doesn't change in this problem. The y -intercept is thenew daily fixed cost.

  $C\left(2\right)=90x+1805$

The new cost function is obtained with the original variable cost and thenew daily fixed cost.

The linear model expressing the cost is as follows $C=90x+1805$ .

Conclusion:

Therefore, the linear model expressing the cost is as follows $C=90x+1805$ .

(c)

To determine

To graph: the model

Answer to Problem 48AYU

The graph was drawn.

Explanation of Solution

Calculation:

The graph of the cost function $C=90x+1805$ is as under

  

Conclusion:

Therefore, the graph was drawn.

(d)

To determine

To find: the cost of manufacturing 14 bicycles in a day

Answer to Problem 48AYU

The cost of manufacturing 14 bicycles in a day is $3605.

Explanation of Solution

Calculation:

Cost of manufacturing 14 bicycles in a day, that is, $x=14$ is as follows

  $\begin{array}{l}C=90\left(14\right)+1805\\ =1260+1805\\ =3065\end{array}$

That is, $3605.

Conclusion:

Therefore, the cost of manufacturing 14 bicycles in a day is $3605.

(e)

To determine

To find: the number of bicycle can be manufactured for $3780.

Answer to Problem 48AYU

21 bicycle can be manufactured for $3780.

Explanation of Solution

Calculation:

As the cost of manufacturing $3780, that is, $C=3780$ ; number of bicycles which can be manufactured is found as follows

  $\begin{array}{l}3780\text{ = }90x+1805\\ 90x=1975\\ x=21.94\end{array}$

That is, 21 bicycles can be manufactured in the given cost.

Conclusion:

Therefore, 21 bicycle can be manufactured for $3780.