Question

Problem 14-15 (All answers were generated using 1,000 trials and native Excel functionality.) 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. (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 corresponding to average demand (60,000 units)? $ 380000 (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 profit associated with the production quantity of 60,000 dolls? $ 180803 How does this compare to the profit corresponding to the average demand (as computed in part a)? The input in the box below will not be graded, but may be reviewed and considered by your instructor. blank (c) 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? When ordering 50,000 units, the average profit is approximately $ 213768 When ordering 70,000 units, the average profit is approximately $ 63360 V (d) Besides mean 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. What trade-offs occur? If required, round Probability of a Loss to three decimal places and Probability of a Shortage to two decimal places. Production Average Profit Standard Maximum Probability of Probability of Quantity Profit Deviation Profit a Loss a shortage 40,000 ard Maximum 50,000 , 300000 60,000 213768 180803 SO63360 $ 188561.8 $ 285465.7 $ 359180.3 70,000 380000 460000

Answer 1

Worksheet to simulate the sales of the Freddy doll using the production quantity of 60000 units:  

First enter the data Mandrell Tov Company Fixed Production Cost $100,000 Unit Variable Cost Unit Selling Pice Unit Surplus Price $34 $42 $10 Production Quantit 60,000 Demand Normal Distribution Mean Standard Deviation 60,000 15,000 Simulation Trials Sales Trial Demand Sales RevenueSurplus SurplusTotal Revenu e Cost Profit The cell formulas for the simulations trials are as follows The cell under Trial Enter 1 for the first simulation trial Simulate the demand (normal distribution) using the NORMINV and RAND functions The minimum of demand and The cell under Demand The cell under Sales The cell under Sales Revenue Multiply sales by the unit selling price The cell under Surplus The cell under Surplus Revenue The cell under Total Cost The cell under Net Profit oduction quantit The surplus of the production quantitjy over the demand Multiply the surplus by the unit surplus rice The fixed cost plus the variable cost The sales revenue plus the surplus revenue minus the total cost

Copy the cells for the first trial down until 500 trials are produced. Note your values wil 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 Tov Com Fixed Production Cost Unit Variable Cost Unit Selling Price Unit Surplus Price $100,000 $34 $42 $10 Production Quant 60,000 Demand Normal Distribution Mean Standard Deviation 60,000 15,000 Simulation Trials Sales Trial Demand Sales Total CostNet Profit RevenueSurplus Surplus Revenue 73.364 25,636 49,615 63.018 72,040 60,000 2,520,000 25,636 $1,076,712 34,364 $343,640 $2,140,000 ($719,648 49,615$2,083,830 10,385 $103,850 $2,140,000 $47,680 60,000 $2,520,000 60,000 2,520,000 $2,140,000 $380,000 499 500 $2,140,000 $380,000 $2,140,000 $380,000 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

b) Simulation of the sales of Freddy doll using a production quantity of 70,000 units Change the production quantity to 70,000 and recalculate the s ummary statistiCs Mandrell Tov Companv Fixed Production Cost Unit Variable Cost Unit Selling Price Unit Surplus Price $100,000 $34 $42 $10 Production Quant 70,000 Demand Normal Distribution Mean Standard Deviation 60,000 15,000 Simulation Trials Sales Trial Demand Sales Net Profit Revenue Surplus Surplus Revenue Total Cost 34,723 57,763 51,571 42,991 59,681 34,723 $1,458,36635,277$352,770 $2,480,000 ($668,864 57,763 $2,426,046 12,237 $122,370 $2,480,000 $68,416 1,571 $2,165,982 18,429 $184,290 $2,480,000 ($129,728 42,991 $1,805,622 27,009 $270,090 $2,480,000 ($404,288 59,681 $2,506,602 10,319 $103,190 $2,480,000 $129,792 499 500 Summary Statistics Mean Profit Standard Deviation Minimum Profit Maximum Profit $63,360 359,180.3 $1,018,080 $460,000

Change the production quantity to 50,000 and recalculate the summary statistics Mandrell Tov Companv Fixed Production Cost Unit Variable Cost Unit Selling Price Unit Surplus Price $100,000 $34 $42 $10 Production Quantit 50,000 Demand Normal Distribution Mean Standard Deviation 60,000 15,000 Simulation Trials Sales Trial Demand Total Cost Sales Net Profit RevenueSurplus Surplus Revenue $0 61,979 38,963 39,616 83,905 36,865 50,000 $2,100,000 38,963 $1,636,446 11,037$110,370 $1,800,000 (S53,184 39,616$1,663,87210,384 $103,840 $1,800,000 (S32,288 50,000 $2,100,000 36,865 $1,548,330 13,135$131,350 $1,800,000 ($120,320 $1,800,000 $300,000 499 $0 $1,800,000 $300,000 500 Summary Statistics Mean Profit Standard Deviatiorn Minimum Profit Maximum Profit $213,768 188,561.8 .037.568 A summary of the different production quantities Production MinimumMaximum Mean Profit Deviation S213,768188,561.8 (1,037,568) S300,000 S180,803285,465. (S1,129,600) S380,000 S63.360 359.180.3 (S1.018,080) S460,000 antit Profit Profit 50,000 60.000 70,000 A more conservative approach with a production quantity of 50,000 has the largest mean profit and the lowest variance. It is recommended that the company should produce a quantity of 50,000 dolls.