Chapter 4.6, Problem 56E

a.

To determine

To find: The cost of the function.

Answer to Problem 56E

The cost of the function is $2000$ .

Explanation of Solution

Given:

The cost of ABC corporation to produce twenty color televisions is $\$3000$ and $\$5000$ to produce sixty color televisions.

Calculation:

The slope of the function is given by subtracting the cost of both the televisions and divided them by the number of televisions. Thus,

  $\begin{array}{c}m=\frac{3000-5000}{20-60}\\ =50\end{array}$

To find the cost of the function substitute the values in the given formula,

  $\begin{array}{c}y=mx+c\\ 3000=50\left(20\right)+c\\ c=2000\end{array}$

Since, $C\left(x\right)=50x+2000$ .

Therefore, the cost of the function is $2000$ .

b.

To determine

To find: The fixed cost and the variable cost per unit.

Answer to Problem 56E

The fixed cost is $2000$ and the variable cost is $50$ .

Explanation of Solution

Given:

The cost of ABC corporation to produce twenty color televisions is $\$3000$ and $\$5000$ .

to produce sixty color televisions.

Calculation:

Fixed cost is the $\text{y-intercept}$ and variable cost is the slope.

Hence, from the above solution,

  $C\left(x\right)=50x+2000$

The $\text{y-intercept}$ is $2000$ and the variable cost is $m=50$ .

Therefore, the fixed cost is $2000$ and the variable cost is $50$ .

c.

To determine

To draw: The sketch graph of the cost function.

Answer to Problem 56E

The graph is shown below.

Explanation of Solution

Given:

The cost of ABC corporation to produce twenty color televisions is $\$3000$ and $\$5000$ to produce sixty color televisions.

Calculation:

The sketch graph of the cost function is shown below.

  

Therefore, the graph is shown above.