You are currently trying to decide between two cost structures for your business: one that has a greater proportion of short$-$term fixed costs and another that is more heavily weighted to variable costs. Estimated revenue and cost data for each alternative are as follows:

Cost Structure

Alternative $1$ Alternative $2$

Selling price per unit $ $50$ $ $50$

Variable cost per unit $2520$

Short$-$term fixed costs per year $25,00030,000$

Required:

$1.$ What sales volume, in units, is needed for the total costs in each cost$-$structure alternative to be the same?

$2.$ Suppose your profit goal for the coming year is $10\%$ of sales $($i$.$e$.,$ operating profit$/$sales $=10\%).$ What sales level in units is needed under each alternative to achieve this goal?

$3.$ Suppose again that your profit goal for the coming year is $10\%$ of sales. What sales volume in dollars is needed under each alternative to achieve this goal?