Problem $16-11($Algorithmic$)$

In preparing for the upcoming holiday season, Fresh Toy Company $($FTC$)$ designed a new doll called The Dougie that teaches children how to dance. The fixed cost to produce the doll is $$100,000.$ The variable cost, which includes material, labor, and shipping costs, is $$34$ per doll. During the holiday selling season, FTC will sell the dolls for $$42$ each. If FTC overproduces the dolls, the excess dolls will be sold in January through a distributor who has agreed to pay FTC $$10$ per doll. Demand for new toys during the holiday selling season is extremely uncertain. Forecasts are for expected sales of $60,000$ dolls with a standard deviation of $15,000.$ The normal probability distribution is assumed to be a good description of the demand. FTC has tentatively decided to produce $60,000$ units $($the same as average demand$),$ but it wants to conduct an analysis regarding this production quantity before finalizing the decision.

Create a what$-$if spreadsheet model using a formula that relate the values of production quantity, demand, sales, revenue from sales, amount of surplus, revenue from sales of surplus, total cost, and net profit. What is the profit corresponding to average demand $(60,000$ units$)?$

$ fill in the blank $1$

Modeling demand as a normal random variable with a mean of $60,000$ and a standard deviation of $15,000,$ simulate the sales of the Dougie doll using a production quantity of $60,000$ units. What is the estimate of the average profit associated with the production quantity of $60,000$ dolls? Round your answer to the nearest dollar.

$ fill in the blank $2$

How does this compare to the profit corresponding to the average demand $($as computed in part $($a$))?$

Average profit is

the profit corresponding to average demand.

Before making a final decision on the production quantity, management wants an analysis of a more aggressive $70,000-$unit production quantity and a more conservative $50,000-$unit production quantity. Run your simulation with these two production quantities. What is the mean profit associated with each? Round your answers to the nearest dollar.

$50,000-$unit production quantity: $ fill in the blank $4$

$70,000-$unit production quantity: $ fill in the blank $5$

In addition to mean profit, what other factors should FTC consider in determining a production quantity?

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Compare the three production quantities $(50,000,60,000,$ and $70,000)$ using all these factors. What trade$-$offs occur? Round your answers to $3$ decimal places.

$50,000$ units: fill in the blank $7$

$60,000$ units: fill in the blank $8$

$70,000$ units: fill in the blank $9$

What is your recommendation?

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