Chapter 1.4, Problem 71E

a .

To determine

To write: the total cost C as a function of the number of units produced.

Answer to Problem 71E

  $C=12.30x+98,000$

Explanation of Solution

Given:

The variable cost for producing the product is $12.30 per unit and the fixed costs are $98,000.

Let x denotes the number of units produced.

And let C represents the total cost of producing x units.

Now, the total cost of producing x units is equal to the sum of fixed cost and the variable cost of x units. Thus,

  $C=12.30x+98,000$

b.

To determine

To write: the equation for the revenue R as a function of the number of units sold.

Answer to Problem 71E

  $R=17.98x$

Explanation of Solution

Given:

The product sells for $17.98.

Let x denotes the number of units sold.

Revenue = Price per unit $\times$ Number of units sold

Since product sells for $17.98 and total x units are sold, so, revenue function is given by:

  $\begin{array}{c}R=17.98\times x\\ =17.98x\end{array}$

c.

To determine

To find: the equation for the profit P as a function of the number of units sold.

Answer to Problem 71E

  $P=5.68x-98,000$

Explanation of Solution

Let x denotes the number of units sold.

From part (a), the cost function is given by $C=12.30x+98,000$ .

From part (b), the revenue function is given by $R=17.98x$ .

Now, it is known that,

Profit = Revenue − Cost

  $\begin{array}{c}P=R-C\\ =17.98x-\left(12.30x+98,000\right)\\ =17.98x-12.30x-98,000\\ =5.68x-98,000\end{array}$