The HighStep Shoe Company operates a chain of shoe stores that sell $10$ different styles of inexpensive$$ men's shoes with identical unit costs and selling prices. A unit is defined as a pair of shoes. Each store has a store manager who is paid a fixed salary. Individual salespeople receive a fixed salary and a sales commission. HighStep is considering opening another store that is expected to have the revenue and cost relationships shown$$ here: HighStep Shoe Company is considering an alternative compensation$$ plan; one in which the sales commissions are discontinued and fixed salaries are raised by a total of $ $15$ comma $500,$ Assume the role of the owner of HighStep Shoe Company. $1.$

As$$ owner, which sales compensation plan would you choose if forecasted annual sales of the new store were at least $10$ comma $000?$ What do you think of the motivational aspect of your chosen compensation$$ plan?

$2.$

Suppose the target operating income is $ $69$ comma $000.$ How many units must be sold to reach the target operating income under$($a$)$ the original$$ salary$-$plus$-$commissions plan and$($b$)$ the$$ higher$-$ fixed$-$salaries$-$only$$ plan? Which method would you$$ prefer? Explain briefly.

$3.$

You open the new store on January$1,2020,$ with the original$$ salary$-$plus$-$commission compensation plan in place. Because you expect the cost of the shoes to rise due to$$ inflation, you place a firm bulk order for $11$ comma $000$ shoes and lock in the $ $37\mathrm{.}00$ price per unit. But toward the end of the$$ year, only $9$ comma $500$ shoes are$$ sold, and you authorize a markdown of the remaining inventory to $ $50$ per unit.$$ Finally, all units are sold.$$ Salespeople, as$$ usual, get paid a commission of $5\%$ of revenues. What is the annual operating income for the$$ store?