Our monogramming subcontractor gets $$14\mathrm{.}00$ for each sweater. Shipping cost $is$ paid $by$ the customer when the order $is$ placed.

$In$ addition $to$ the cost data, you also have some demand information, $as$ shown $in$ Exhibit $20\mathrm{.}13.$ The exact sales numbers for last year are given. The exhibit indicates the retail $orfull$ price$$ sales for the sweaters that were sold for $$127$ each. Sweaters that $we$ had $at$ the end $of$ the season were sold through eBay for $$46$ each and were not monogrammed. Keep $in$ mind that the retail sales numbers $do$ not accurately reflect actual demand since they stocked out $of$ the OSU sweaters toward the end $of$ the season.

$As$ for advertising the sweaters for next season, Rhonda $is$ committed $to$ using the same approach used last year. The firm placed ads $in$ the football program sold $at$ each game. These worked very well for reaching those attending the games, but she realized there might $be$ ways $to$ advertise that would open sales $to$ more alumni. She has hired a market research firm $to$ help identify other advertising outlets but has decided $to$ wait $at$ least another year $to$ try something different.

Forecasting demand $is$ a major problem for the company. You have asked Rhonda and Steve $to$ predict what they think sales might $be$ next year. You have also asked the market research firm $to$ apply their forecasting tools. Data $on$ these forecasts are given $in$ Exhibit $20\mathrm{.}13.To$ generate some statistics you have averaged the forecasts and calculated the standard deviation for each school and $in$ total.

Based $on$ advice from the market research firm, you have decided $to$ use the aggregate demand forecast and standard deviation for the aggregate demand. The aggregate demand was calculated $by$ adding the average forecast for each item. The aggregate standard deviation was calculated $by$ squaring the standard deviation for each item $(thisis$ the variance$),$ summing the variance for each item, and then taking the square root $of$ this sum. This assumes that the demand for each school $is$ independent, meaning that the demand for Ohio State $is$ totally unrelated $to$ the demand $at$ Michigan and the other schools.

You will allocate your aggregate order $to$ the individual schools based $on$ their expected percentage $of$ total demand. You discussed your analysis with Rhonda and Steve and they are $OK$ with your analysis. They would like $to$ see what the order quantities would $beif$ each school was considered individually.

You are curious $asto$ how much Rhonda and Steve made $in$ their business last year. You $do$ not have all the data, but you know that most $of$ their expenses relate $to$ buying the sweaters and having them monogrammed. You know they paid themselves $$50,000$ each and you know the rent, utilities, insurance, and a benefit package for the business was about $$25,000.$

$a.$ What was the net pre$-$tax profit for their business last year, after deducting salary and overhead? $(Do$ not round intermediate calculations. Round your answer $to$ the nearest dollar amount.$)$

$b.If$ they must pay $50\%in$ taxes after deducting their venture capital firm payment, what was the increase $in$ cash that their business accrued last year? $(Do$ not round intermediate calculations. Round your answer $to$ the nearest dollar amount.$)$

Exhlblt $20\mathrm{.}12$

Exhlbit $20\mathrm{.}13$

$*336$ sweaters were sold through eBay for $$46$ each $(the$ customer pays shipping $on$ all orders$).$

$**$ Calculated assuming the demand $at$ each school $Is$ independent $=\sqrt[\phantom{2}]{{\displaystyle \underset{i=1}{\overset{N}{}}}{}_i^2}$

Our monogramming subcontractor gets $$14\mathrm{.}00$ for each sweater. Shipping cost $is$ pald $by$ the customer when the order $is$ placed. $In$ addition $to$ the cost data, you also have some demand Information, $as$ shown $In$ Exhibit $20\mathrm{.}13.$ The exact sales numbers for last year

are given. The exhibit indicates the retall $or$ "full price" sales for the sweaters that were sold for $$127$ each. Sweaters that $we$ had $at$ the

end $of$ the season were sold through eBay for $$46$ each and were not monogrammed. Keep $in$ mind that the retall sales numbers $do$

not accurately reflect actual demand since they stocked out $of$ the OSU sweaters toward the end $of$ the season.

$As$ for advertising the sweaters for next season, Rhonda $Is$ committed $to$ using the same approach used last year. The firm placed ads

$In$ the football program sold $at$ each game. These worked very well for reaching those attending the games, but she realized there

might $be$ ways $to$ advertise that would open sales $to$ more alumnI. She has hired a market research firm $to$ help identify other

advertising outlets but has decided $to$ walt $at$ least another year $to$ try something different.

Forecasting demand $is$ a major problem for the company. You have asked Rhonda and Steve $to$ predict what they think sales might $be$

next year. You have also asked the market research firm $to$ apply their forecasting tools. Data $on$ these forecasts are given $in$ Exhibit

$20\mathrm{.}13.To$ generate some statistics you have averaged $t$