Question

Problem 12-11

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.
   
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-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:
   
   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. In this case, production is 60000 and all is considered to be sold in normal scenario with zero in surplus category

So revenue from sales = 60000 X 42 = $ 2,520,000

Total cost = 100,000 + 34X60000 = $2,140,000

So total profit = $380,000

b. We can simulate demand as a normal random variable with a mean of 60,000 and a standard deviation of 15,000

Let us take some 100 such scenarios in excel

We can use Norm.inv function in excel as norm.inv (probability, mean, sd) = norm.inv (rand(), 60000,15000)

rand() gives a random no between 0 and 1 which is required to randomly assign a probability factor so that the function can arrive at a random no for demand based on mean of 60000 and SD of 15000

One we copy above formula in 100 rows of excel, please ensure to copy and pase the column as values since in excel these nos will keep changing everytime we press enter.

Now since production is 60000 and demand varies, if production is greater than demand, the excess qty will be sold as surplus else if the demand is greater than equal to production, there will be normal sales

For these 100 scenarios, the table is given below: Note that the cost is constant for each case viz., 2,140,000

The average of the last column for profit comes out as $203,243 which is significantly less than the profit calculated in part a viz., $380,000

c. We run the above simulation in excel with production of 70,000 and 50,000. The two tables are given below. The deamnd scenarios for the100 cases is kept same. only the third column of production is changes from 6000 to 7000 and then 5000

50,000-unit production quantity: $ 237,623

70,000-unit production quantity: $ 106,953

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

The other factors to be considered are whether FTC is making enough provisions for breakdown in production owing to which there may be a shortage in meeting the demand

In this case, there will be tradeoff between shortage in meeting the demand vs selling excess quantities above demand at lower surplus value of $10

Looking at the average profit nos, between the three production quantities of 50000, 60000 and 70000, since the mean profit is the higest for the lowest qty, one should go for production of 50000