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Written Problem 3) From page 2 of the In-Class Exercises Simulations document. In preparing for the upcoming holiday season, Fresh Toy Company (FTC) designed a new doll called The Rougie 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 dolls. 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. Suppose that, if demand exceeds production, the firm can outsource those units at a cost of $40/doll. (adapted from Problem 15 in Chapter 14) a) Write an equation that models the profit for this firm from the upcoming holiday season, with q=dolls produced, d-dolls demanded in the holiday selling season, o=# dolls outsourced, and e=excess production b) What is the best case profit (assuming no outliers)? c) What is the worst case profit (assuming no outliers)? d) What is the base case profit? e) Modeling demand as a normal random variable, simulate the sales of The Dougie doll when production is 60,000 dolls using the following random numbers: i. When r1=0.4325, how many dolls will be sold in the holiday season? Sold in January? ii. When r=0.9983, how many dolls will be sold in the holiday season? Sold in January? 1 Now compute the profit associated with each of these simulations i. When r1=0.4325, what is the firm's profit? 11. When rz=0.9983, what is the firm's profit? Page 3 Written Problem 3) From page 2 of the In-Class Exercises Simulations document. In preparing for the upcoming holiday season, Fresh Toy Company (FTC) designed a new doll called The Rougie 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 dolls. 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. Suppose that, if demand exceeds production, the firm can outsource those units at a cost of $40/doll. (adapted from Problem 15 in Chapter 14) a) Write an equation that models the profit for this firm from the upcoming holiday season, with q=dolls produced, d-dolls demanded in the holiday selling season, o=# dolls outsourced, and e=excess production b) What is the best case profit (assuming no outliers)? c) What is the worst case profit (assuming no outliers)? d) What is the base case profit? e) Modeling demand as a normal random variable, simulate the sales of The Dougie doll when production is 60,000 dolls using the following random numbers: i. When r1=0.4325, how many dolls will be sold in the holiday season? Sold in January? ii. When r=0.9983, how many dolls will be sold in the holiday season? Sold in January? 1 Now compute the profit associated with each of these simulations i. When r1=0.4325, what is the firm's profit? 11. When rz=0.9983, what is the firm's profit? Page 3