Question

question
a sportswear manufacturer is introducing a new line of sneakers. to introduce the new line, the company must pay out a fixed cost of $1.5 million for advertising and equipment, plus there is a cost of 40 cents per pair of sneakers manufactured. it plans to sell the sneakers for $75 per pair.
let $x$ be the number of pairs of sneakers manufactured. what is the total revenue at breakeven? give your answer to the nearest thousand.
provide your answer below:
$

Explanation:

Step1: Set up cost and revenue functions

Cost function $C(x)=1500000 + 0.4x$, Revenue function $R(x)=75x$.

Step2: Find break - even point

At break - even, $C(x)=R(x)$. So $1500000 + 0.4x=75x$.
Rearranging gives $75x-0.4x = 1500000$, i.e., $74.6x = 1500000$.
Then $x=\frac{1500000}{74.6}\approx20107.24$.

Step3: Calculate total revenue at break - even

Substitute $x$ into $R(x)$. $R(20107.24)=75\times20107.24 = 1508043\approx1510000$.

Answer:

$1510000$