Answer
(a.) $C(x)=60,000+200x$.
(b.) $R(x)=450x$
(c.) $(240,108000)$.
When we produce and sold $240$ desks, the cost and revenue are $\$108,000$.
Work Step by Step
The given values are
Fixed cost is $=\$60,000$.
Variable cost is $=\$200$ to produce each desk.
Revenue per $=\$450$.
(a.) Cost function $C$.
Cost function $=$ Fixed cost plus variable cost.
In the equation form
$\Rightarrow C(x)=60,000+200x$
(b.) Revenue function $R$.
Revenue function $=$ Revenue per desk $\times$ number of desks sold.
In the equation form
$\Rightarrow R(x)=450x$
(c.) Break-even point.
The break-even point is when both cost and revenue functions are equal.
Equate both functions and solve for $x$.
$\Rightarrow R(x)=C(x)$
$\Rightarrow 450x=60,000+200x$
Subtract $200x$ from both sides.
$\Rightarrow 450x-200x=60,000+200x-200x$
Simplify.
$\Rightarrow 250x=60,000$
Divide both sides by $250$.
$\Rightarrow \frac{250x}{250}=\frac{60,000}{250}$
Simplify.
$\Rightarrow x=240$
Substitute the value of $x$ into the revenue function.
$\Rightarrow 450(240)$.
$\Rightarrow 108,000$.
Hence, the break even point is $(240,108000)$.
When we produce and sold $240$ desks, the cost and revenue are $\$108,000$.
