In preparing for the upcoming holiday season, Fresh Toy Comparly (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 $31 per doll, During the holiday selling season, FrC will sell the dolls for $39 each, If FIC overproduces the dolls, the excess dolis will be sold in January through a distributor who has agreed to pay FIC $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. FrC 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) Determine the equation for computing FTC's profit for given values of the reievant parameters (e.g., demand, production quantity, etc.). Using this equation, compute FTCs profit (in dollars) when realized dernand is equal to 60,000 (the average demand). s. (b) Modeling demand as a normal random variable with a mean of 60,000 and a standard deviation of is,000, simulate the sales of the Dougie doll using a production quantity of 60,000 units: What is the estimate of the average proft (in dollars) asvociated with the production quantity of 60,000 dolis? (Use at least 1,000 trals. Round your answer to the nearest integet) $ (c) Compare the average profit estamated by sumulation in part (b) to the profit calculation in part (a). The average profit from the simulation is greater than the profit computed in part (a) The average profit from the simulation is less than the profit computed in part (a). Explain why they differ: Profit is limited by the production quantity, so lower than average demand does not correspond to lower profits, but higher demand will iead to higher profits. Since the demand is being modeled as a normal random varable, the sample mean profit will always tend to be lower than the true mean profit. Profit is limited by the production quantity, so higher than average demand does not correspond to higher profits, but lower demand will lead to lower profits. Since the demand is being modeled as a normal random variable, the sample mean profit will always tend to be higher than the true mean profit. Explain why they differ. Profit is limited by the production quantity, so lower than average demand does not correspond to lower profits; but higher demand will lead to higher profits. Since the demand is being modeled as a normal random variable, the sample mean profit will always tend to be lower than the true mean profit. Profit is limited by the production quantity, so higher than average demand does not correspond to higher profits, but lower demand will lead to lower profits. Since the demand is being modeled as a normal random variable, the sample mean profit will always tend to be higher than the true mean profit. (d) 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. (Use at least 1,000 trials. Round your answers to the nearest integer.) What is the mean profit (in dollars) associated with 50,000 units? What is the mean profit (in dollars) associated with 70,000 units? (e) In addition to mean profit, what other factors should FTC consider in determining a production quantity? (Select all that apply) profit standard deviation stock market probability of a shortage probability of a loss gut feeling