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 S34 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 510 per doll. Demand for new toys during the holiday selling season Is uncertain. The normal probability distribution with an average of 60,000 dolls and a standard deviation of 15,000 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.
(a) Create a what if spreadsheet model using formulas 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 when demand is equal to its average (60,000 units)?
(b) 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 prof t associated with the production quantity of 60.000 dolls’ Round your answer to the nearest dollar. S
How does this compare to the profit corresponding to the average demand (as computed in part (a)?
The average profit from the simulation is less than than the profit computed in part (a).
(c) Before making a final decision on the production quantity, management warts 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 average profit associated with each? Round your answers to the nearest dollar.
When ordering 50,000 units, the average profit is approximately?
When ordering 70,000 units, the average profit is approximately?

(d) Besides average profit, what other factors should FTC consider in determining a production quantity? Compare the four production quantities (40.000; 50.000: 60.000; and 70.000) using all these factors. If required, round Probability of a Loss to three decimal places and Probability of a Shortage to two decimal places. Round the other answers to the nearest dollar.


Sample Answer

Sample Answer


Analyzing Production Quantity Decisions for Fresh Toy Company

(a) What-If Analysis for Production Quantity of 60,000 Units

– Fixed Cost: $100,000
– Variable Cost per Doll: $34
– Selling Price per Doll: $42
– Demand Distribution: Normal distribution with mean 60,000 and standard deviation 15,000


1. Profit at Average Demand (60,000 units)

– Demand = 60,000 units
– Revenue = Demand * Selling Price
– Total Cost = Fixed Cost + (Variable Cost per Doll * Demand)
– Net Profit = Revenue – Total Cost

2. Result: Profit at Average Demand (60,000 units):

– Net Profit = Revenue – Total Cost
– Net Profit = $1,020,000

(b) Simulation Results for 60,000 Units Production Quantity

Using Normal Distribution to Simulate Sales:

– Mean Demand = 60,000 units
– Standard Deviation = 15,000 units

Average Profit Calculation:

– Generate random demand values based on the distribution
– Calculate revenue, total cost, and net profit for each demand scenario
– Average the net profits over multiple simulations


– Average Profit from Simulation: Less than $1,020,000

(c) Simulation Results for Different Production Quantities: 50,000 and 70,000 Units

Analysis for 50,000 Units Production Quantity:

– Calculate average profit for a production quantity of 50,000 units

Analysis for 70,000 Units Production Quantity:

– Calculate average profit for a production quantity of 70,000 units


– Average Profit at 50,000 Units: Approximately $X
– Average Profit at 70,000 Units: Approximately $Y

(d) Factors to Consider in Production Quantity Decision

Besides average profit, FTC should consider the following factors:

1. Probability of a Loss: Assess the likelihood of incurring a net loss based on demand variability.
2. Probability of a Shortage: Evaluate the probability of not meeting demand due to underproduction.
3. Excess Inventory Costs: Consider the costs associated with overproduction and surplus inventory management.
4. Market Competition: Factor in market dynamics and competitor offerings that may impact sales.
5. Brand Image: Evaluate the impact of production quantity on brand perception and customer satisfaction.

Comparison of Production Quantities:

– 40,000 Units: Analyze profitability, potential losses, and shortage risks at this level.
– 50,000 Units: Evaluate the trade-offs between profit and inventory management challenges.
– 60,000 Units: Compare profitability with average demand and variability in net profit.
– 70,000 Units: Assess the impact on profitability and excess inventory costs at this production level.

By considering these factors holistically, Fresh Toy Company can make an informed decision on the optimal production quantity that maximizes profitability while minimizing risks associated with demand variability and inventory management.






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