Answer
a. $C(x)=400,000 +20x$,
b. $R(x)=100x$
c. $P(x)=80x-400,000$
d. $x=5000$
Work Step by Step
The function cost is the fixed cost plus the cost of producing each item times the number of items produced. the revenue function is the number of items sold times the price the items sold for. Profit function is the revenue function minus the cost function. The break even point is the point in which the revenues equals the cost. Therefore, the profit is $0$ at that point.
a. $C(x)=400,000 +20x$,
b. $R(x)=100x$
c. $P(x)=R(x)-C(x)$,
$P(x)=100x-400,000 -20x$,
$P(x)=80x-400,000$
d.
$0=80x-400,000$,
$400,000=80x$,
$x=5000$
