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. if the firm only manages to sell 15,000 sneakers, what is the total loss? provide your answer below:

Explanation:

Step1: Calculate total cost

The fixed - cost is $1500000$, and the variable cost per pair is $0.4$. For $x = 15000$ pairs, the variable cost is $0.4x$. So the total cost $C=1500000 + 0.4\times15000=1500000+6000 = 1506000$.

Step2: Calculate total revenue

The selling price per pair is $75$. For $x = 15000$ pairs, the total revenue $R = 75\times15000=1125000$.

Step3: Calculate total loss

Loss $L=C - R$. Substitute $C = 1506000$ and $R = 1125000$ into the formula, we get $L=1506000 - 1125000=941000$.

Answer:

$941000$