Answer
$C(x)=0.15x+350$
$R(x)=0.50x$
$P(x)= 0.35x-350$
Work Step by Step
A cost function of the form $C(x)=mx+b$ is called a linear cost function,
the variable cost is $mx$ and the fixed cost is $b$.
The slope $m$, the marginal cost, measures the incremental cost per item.
If $R(x)$ is the revenue from selling $x$ items at a price of m each, then
$R$ is the linear function $R(x)=mx$
and the selling price $m$ can also be called the marginal revenue.
Profit $=$ Revenue-Cost,$\qquad P(x)=R(x)-C(x)$
Breakeven occurs when $P=0$, or $R(x)=C(x)$.
The break-even point is the number of items $x$ at which break even occurs.
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Reading the text interpret terms
marginal cost$ =\$ 0.15x$,
fixed cost = $\$ 350$
marginal revenue = unit sale price $= \$ 0.50$
Cost function, $C(x)=0.15x+350$
Revenue function: $R(x)=0.50x$
Profit:
$P(x)$ = $R(x)-C(x)=0.50x-(0.15x+350)$
$P(x)= 0.35x-350$
