$34)$ Sail Safe currently sells motor boats for $$60,000.$ It has costs of $$46,500.$ A competitor is bringing a new motor boat to the market that will sell for $$55,000.$ Management believes it must lower the price to $$55,000$ to compete in the market for motor boats. The marketing department believes that the new price will cause sales to increase by $12\mathrm{.}5\%,$ even with a new competitor in the market. Sail Safe's sales are currently $2,000$ motor boats per year. $3$

Required:

a$.$ What is the target cost for the new target price if target operating income is $20\%$ of sales?

b$.$ What is the change in operating income if marketing department is correct and only the sales price is changed?

c$.$ What is the target cost if the company wants to maintain its same income level, and marketing department is correct?