Question

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.

1. Create a what-if spreadsheet model using a formula that relates 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)?
   
   $  
   
2. 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.
   
   $  
   
   How does this compare to the profit corresponding to the average demand (as computed in part (a))?
   
   The average profit is less than the profit corresponding to average demand.
   
3. 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: $  
   
   70,000-unit production quantity: $  
   
4. 
   Compare the three production quantities (50,000, 60,000, and 70,000) using all these factors. What trade-off occurs for the probability that a shortage occurs? Round your answers to 3 decimal places.
   
   50,000 units:
   
   60,000 units:
   
   70,000 units:

Answer 1

a)

What-if spreadsheet model is as follows:

EXCEL FORMULA:

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b)

Spreadsheet model is following:

EXCEL FORMULA:

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c)

Model for production quantity of 50,000 units is following:

Model for production quantity of 70,000 units is following:

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d)

The trade-off for the probability of shortage is the probability of loss. Higher the probability of shortage, the lower the probability of loss and vice versa

Probability of loss is following:

50,000 units: 0.087

60,000 units: 0.222

70,000 units: 0.399