Question

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.

1. 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)?
   
             $__________
   
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))?
   
   Average profit is __________ the profit corresponding to average demand. (Average Profit is Dropdown = less than, more than, equal to)
   
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. In addition to mean profit, what other factors should FTC consider in determining a production quantity?
   
   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: __________
   
   60,000 units: __________
   
   70,000 units: __________
   
   What is your recommendation?

Answer 1

a)

What-if spreadsheet model is as follows:

EXCEL FORMULA:

Profit corresponding to average demand of 60,000 dolls = $ 380,000

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b)

Simulation model is as follows:

EXCEL FORMULA:

Using simulation model, Average profit associated with production quantity of 60,000 dolls = $ 188,838

Average profit is ____less than ____ the profit corresponding to average demand.

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c)

To simulate profit for production quantity of 50000 and 70000 dolls, change the value of Q in cell E11 in the simulation model

For Q = 50,000

----------------------

For Q = 70,000

50,000-unit production quantity: $ 227,049

70,000-unit production quantity: $ 66,751

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d)

The other factors that should be considered are probability of shortage and probability of loss.

Production quantity	Probability of shortage	Probability of loss
50,000	0.73	0.102
60,000	0.51	0.225
70,000	0.25	0.402

Recommendation: We see that average profit corresponding to production quantity of 50,000 dolls is the highest. Furthermore, probability of loss is the lowest for this quantity. So, recommended production quantity is 50,000 dolls