Answer
a) The cost function is $ C\left( x \right)=360,000\text{+850}x $.
b) The revenue function is $ R\left( x \right)=\text{1150}x $.
c) The break-even point is $\left( 1200,138000 \right)$. This means that 1200 computers are required to be sold to make $\$138,000$ that is equivalent to the fixed cost of the company.
Work Step by Step
a) Let x be the number of computers that are produced. The cost of each computer is $\$850$ and the fixed cost of the computer is $\$360,000$. Hence, compute the cost of x computers by multiplying the number of computers that is x with the costing of the computer and adding the fixed cost to the resultant figure.
The total variable cost of the computers will be 850x.
And the total cost is the sum of fixed cost and cost of producing x computers.
Compute the cost function as follows:
Cost function, $ C\left( x \right)=\text{fixed cost}+\text{850}x $
Thus, the cost function is $ C\left( x \right)=360,000\text{+850}x $.
(b)
Let x be the number of computers that are sold. Consider the selling cost of a desk to be $1150$ and hence the total selling cost of x desks is: $\text{1150}x $.
The revenue function is given below,
$\begin{align}
& R\left( x \right)=\text{Revenue per computer}\times \text{number of computer for sale} \\
& =1,150\times x
\end{align}$.
Therefore, the revenue function is:
$ R\left( x \right)=\text{1150}x $
(c)
We have the cost function, $ C\left( x \right)=360,000\text{+850}x $ and revenue function, $ R\left( x \right)=\text{1150}x $.
For determining the break-even points, the condition is that the cost and revenue function must be equal,
that is $ C\left( x \right)=R\left( x \right)$
$\begin{align}
& 360,000\text{+850}x=1150x \\
& 1150x-850x=360000 \\
& 300x=360000 \\
& x=1200
\end{align}$
Put the value of x in the revenue function as shown below:
$\begin{align}
& R\left( x \right)=\text{1150}\times 1200 \\
& =138000
\end{align}$
Hence, the break event point is $\left( x,R\left( x \right) \right)=\left( 1200,138000 \right)$.
This means that the break-even point occurs when $1200$ computers are produced and sold. Thus, this is a point where both cost and revenue are the same.
