Question

trendy t-shirts has decided to manufacture a new design. it will cost $400 plus $3 per shirt to produce them, and trendy plans to spend $5000on advertising. the shirts will sell for $12 each A. how many shirts must be sold to break even (total cost equals income from sales)? B . what is trendy's income (or total cost) for that many shirts?

Answer 1

Trendy T-shirts needs to sell 600 shirts to break even. Both the total cost and the income for these 600 shirts are $7200.

Step-by-step explanation:

To determine how many t-shirts must be sold to break even, we need to calculate the total cost and set it equal to the revenue from shirt sales. The total cost consists of a fixed cost for manufacturing, which is $400, and the advertising expense, which amounts to $5000. Since each shirt has a variable production cost of $3, we can express the total cost (TC) for x shirts as TC = $400 + $3x + $5000, which simplifies to TC = $5400 + $3x.

The revenue (R) from selling x shirts at $12 each is R = $12x. To break even, the total cost must equal the revenue, so $5400 + $3x = $12x. Solving for x gives us x = $5400 / ($12 - $3) = $5400 / $9 = 600 shirts.

For part B, the income for 600 shirts sold at $12 each is just the total revenue, which is 600 * $12 = $7200. Since this amount is equal to the costs when breaking even, the total cost for 600 shirts is also $7200.

Answer 2

I added 5000 400 12 3 and got 5415