In preparing for the upcoming holiday season, Mandrell Toy Company designed a new doll called Freddy. 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, Mandrell will sell the dolls for $42 each. If Mandrell overproduces the dolls, the excess dolls will be sold in January through a distributor who has agreed to pay Mandrell $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.

a. Create a worksheet similar to the inventory worksheet in Figure. Include columns showing demand, sales, revenue from sales, amount of surplus, revenue from sales of surplus, total cost, and net profit. Use your worksheet to simulate the sales of the Freddy doll using a production quantity of 60,000 units. Using 500 simulation trials, what is the estimate of the mean profit associated with the production quantity of 60,000 dolls?

b. 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? What is your recommendation on the production of the Freddy doll?

c. Assuming that Mandrell’s management adopts your recommendation, what is the probability of a stock-out and a shortage of the Freddy dolls during the holiday season?

FIGURE

EXCEL WORKSHEET FOR THE BUTLER INVENTORYPROBLEM

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PortaCom Risk Analysis Lil 3 Sel ling Price per Unit 4 Administrative Cost $249 5400,000 600,000 5 Advertising Cost 7 Direct Labor Cost wer Parts Cost (Uniform Distribution) $80 S100 Upper Smallest Value 9Random No. Random No. Cost per Unit Largest Value 0.0 12 13 14 15 0.3 0.7 0.9 $43 $44 $45 $46 $47 0.7 0.9 Demand (Normal Distribution) Mean Std Deviation 15000 4500 17 Simulation Trials 18 Direct Labor Parts Cost per Unit $85.36 91.68 93.35 $98.56 $88.36 First-Year Demand 17.366 12,900 20,686 0.888 14,259 20 21 Trial Cost per Un Profit 1,025,570 $461.828 $1.288,906 24 648,911 ($71.739) S1,110952 $703.118 45 516 517 18 519 520 521 496 497 498 499 $94.38 $90.85 90.37 92.50 19.257 14,920 13.471 18,614 43 1,056.847 523 524 525 526 527 Summary Statistics Mean Profit Standard Deviation Minimum Profit Maximum Profit Number of Losses Probability of Loss $698.457 ($785,234) $2.367.058