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. 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 less than  the profit corresponding to average demand.
   
2. 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: $  
   
3. 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

ANSWER:

As per the given Question

a) Worksheet to simulate the sales of the Freddy doll using the production quantity of 60,000 units: First enter the data. Mandrell Toy Company Fixed Production Cost Unit Variable Cost Unit Selling Price Unit Surplus Price $100,000 $34 $42 $10 Production Quantity 60,000 Demand (Normal Distribution) Mean 60,000 15,000 Standard Deviation Simulation Trials Sales Surplus Total Net Surplus Trial Demand Sales Profit Revenue Revenue Cost

The cell formulas for the simulations trials are as follows: The cell under Trial Enter 1 for the first simulation trial. Simulate the demand distribution) using the NORMINV and RAND functions The minimum of demand and production quantity Multiply sales by the unit selling price. The surplus of the production quantity over the demand. (normal The cell under Demand The cell under Sales The cell under Sales Revenue The cell under Surplus The cell under Surplus RevenueMultiply the surplus by the unit surplus The cell under Total Cost price The fixed cost plus the variable cost. The sales revenue plus the surplus The cell under Net Profit revenue minus the total cost.

Copy the cells for the first trial down until 500 trials are produced. Note your values will be different because RAND picks a random number. The spreadsheet below has a majority of the trials hidden. Use the AVERAGE function to find the mean net profit. Mandrell Toy Company Fixed Production Cost Unit Vaniable Cost Unit Selling Price Unit Suplus Price $100,000 $34 $42 $10 Production Quantity 60,000 Demand (Normal Distribution) 60,000 Mean Standard Deviation 15,000 Simulation Trials

Simulation Trials Sales Surplus Revenue Total Cost Net Profit Trial Demand Sales Surplus Revenue $2,140,000 $380,000 $2,520,000 $1,076,712 34,364 $343,640 $2,140,000 ($719,648) $2,083,830 10,385 $103,850 $2,140,000 $0 1 73,364 25,636 60,000 25,636 0 2 49,615 49,615 $47,680 $2,140,000 $380,000 $2,140,000 $38o,000 499 63,018 72,040 60,000 60,000 $2,520,000 $2,520,000 $0 500 $0 Summary Statistics Mean Profit Standard Deviation Minimum Profit Maximum Profit $180,803 285,465.7 ($1,129,600) $380,000 Using the 500 simulation trials, the estimated mean profit is S180,803.

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