Question

(All answers generated on the Analytic Solver Platform using 10,000 trials and random seed 1994.)

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.

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.

Average Profit ?

Profit Standard Deviation ?

Maximum Profit ?

Probability of a Loss ?

Probability of a Shortage ?

Answer 1

Other factors to consider when evaluating a production quantity includes probability of a loss, profit standard deviation, and probability of a shortage. The table below represents all the factors: Production Average Profit Standard Maximum Probability of a Probability of a Quantity Profit Deviation Profit Loss Shortage 5220,000 0.037 $300,000 0.098 $380,000 0.214 460,000 0.385 40,000 $199,651 $87,043 $227,462 $172,343 $188,508 $280,245 $67,462 $379,164 0.91 50,000 0.75 60,000 0.50 70,000 0.25 Lower production quantities reduce the downside but also limit the upside. Producing 50,000 units generates the highest expected profit of these alternatives, but also results in a 75 percent chance of a shortage. If this low service level is acceptable, then this is probably the best option.