Question $1)$

$($a$)$The owners of Le trou de l$$argent of Trois$-$Rivi$$res$,$ which specializes in high$-$end snowmobiles, are piloting a new sales approach: They$$ve opened a small pop$-$up shop across from the food court $($the highest traffic area$)$ in the Champlain Mall in Moncton. It will operate October through January. They$$ll carry only the most high$-$performing and expensive models, such as the Yamaha Sidewinder S$-$TX and the Alpina Superclass $1\mathrm{.}2$LVVT$,$ each of which will set you back $$30,000$ all$-$in$.$ They will have only six models on display and only a handful more in the backroom. They hope to sell $100$ of the snow machines during the season $$and since the season equals their sales year, they thus expect to sell $100$ for the year. Given the square$-$footage of the Moncton store, and the extra$-$high rate paid for the prime location and short$-$term lease $($during the most important sales quarter of the year$),$ carrying costs are estimated at $$6,000$ per snowmobile $($annualized$).$ When they order, they$$ll purchase from a wholesaler in Montr$$al that will charge them a flat fee of $$1,500$ per order, no matter how many snowmobiles they order. Given all this information, what is their optimal order size?

$($b$)$ Based on data collected from ATV sales in their Trois$-$Rivi$$res store, management at Le trou de l$$argent expect $25\%$ of the Moncton sales to be in cash$$some rich people just pay for these things in cash! However, they will extend $30$ days of credit to customers, and that will amount to about $60\%$ of sales, and $60$ days of credit to preferred customers, who will make up $15\%$ of sales. They$$ve hired Benny the Loan Shark to handle their receivables and so do not expect any late payments or bad debt. Here is the four month sales forecast $($in thousands of dollars$)$:

October$=150,$ November$=480,$ December$=1680,$ January$=690$ Build a complete Receivables Budget through the end of March and tell me specifically what receivables will be at the end of December.

$($c$)$ The anticipated cash situation is this: As far as inventory purchases are concerned, they generally run $50\%$ of sales, and the purchasing agent at Le trou de l$$argent pays for $75\%$ of that in cash, and the remaining $25\%$ is paid within $30$ days. The company has operating payments of $$47,500$ per month during the operating months $($October through January$).$ Capital outlays will consist of $$125,000$ in October for display equipment for the new store. Financial costs include $$22,500$ that is being put into a GIC monthly during the four months of operation. $($The GIC is separate from the company$$s bank account and is used to accumulate money for tax purposes.$)$ Anticipating a cash crunch, management has already lined up a $$1,000,000$ bank loan for December. The bank loan is to be paid back during January through March, at the rate of $340,000$ per month. Develop a cash budget showing money flowing into and out of Le trou$$s bank account for six months: October through March.

$($d$)$ Finally, develop a short$-$term financing schedule for the four operating months $($October through January$).$ Assume the mangers want to have a cash balance of $$100,000$ in the bank account at the start of every month