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 >=, <=, or =(Chose one) to 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. In addition to mean profit, what other factors should FTC consider in determining a production quantity?
   
   The input in the box below will not be graded, but may be reviewed and considered by your instructor.
   
   
   
   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?
   
   The input in the box below will not be graded, but may be reviewed and considered by your instructor.
   

Answer 1

(a) The spreadsheet model is as follows:

(b) Based on simulation result,

Estimated Average profit associated with production of 60,000 units = $ 192,014

Without simulation, Average profit associated with production and demand of 60,000 units = 60000*(42-34)-100000 = $ 380,000

Average profit is __ <= __   to the profit corresponding to average demand.

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

(c)

Estimated profit with 70000 units of production = 45,547

Estimated profit with 50000 units of production = 224,676

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

(d)

Comparing the three production quantities, we see that trade-offs occur in terms of Surplus and Shortage. If the production is greater than demand, then it results in surplus and if it is lesser than demand, then it leads to shortage. Both surplus and shortage incur cost.

Considering the trade-offs of surplus and shortage, a production quantity of 50,000 units gives the highest average estimated profit.

Recommendation is to produce 50,000 units