Sun Sports Inc. has several kiosks in large and medium$-$sized shopping centers that sell various styles of sports hats for men and women, all at the same price. In addition to the regular salary, the company pays a good commission to its salespeople so that they work hard and are proactive in sales. The following cost and sales price information is representative of each kiosk individually.

Data Per Hat

Sales Price $$42\mathrm{.}00$

Variable Costs

Cost Per Hat $$16\mathrm{.}00$

Sales Comission $$1\mathrm{.}50$

Total Variable Cost $$17\mathrm{.}50$

Costo Annual

Fixed Costs

Salaries $$39,000$

Kiosk Rent $$23,000$

Publicity $$56,000$

Total Fixed Costs $$118,000$

The company wants to review its policies and provide additional incentives to strengthen sales. Provide management with the following analysis of their stores:

$1.$ Calculate the break$-$even point in units and sales dollars of a kiosk.

$2.$ Prepare a cost$-$volume$-$profit graph that shows the revenue and costs of a kiosk from $0$ to $30,000$ caps and the break$-$even point.

$3.$ Present the net operating results $($net profit or loss$)$ if $9,000$ hats are sold per year.

$4.$ The company is evaluating the possibility of offering a commission of $$1\mathrm{.}50$ per hat sold to the kiosk supervisor $($in addition to the sales commissions paid to salespeople at the kiosk$).$ Determine the new break$-$even point in sales dollars and units sold if this commission is added.

$5.$ Instead of the previous $$1\mathrm{.}50$ commission per hat sold, another alternative that the company wants to evaluate is to offer the supervisor only $$1\mathrm{.}50$ for each hat sold in excess of the break$-$even point. If only this commission is applied, what would be the net operating result $($net profit or loss$)$ if $12,000$ hats are sold per year?

$6.$ Another third alternative, instead of the previous ones, is to completely eliminate sales commissions and increase fixed salaries by an additional $$22,000$ annually:

a$.$ Presents the break$-$even point in dollars and sales units for this alternative.

b$.$ Explain whether or not you would recommend this alternative and why.