Complete question:
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) What is the profit corresponding to average demand (60,000 units)?
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? Round your answer to the nearest dollar.
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? Round your answers to the nearest dollar. 50,000-unit production quantity: $ 70,000-unit production quantity:
D) In addition to mean profit, what other factors should FTC consider in determining a production quantity? Compare the three production quantities (50,000, 60,000, and 70,000) using all these factors. What trade-off occurs for the probability that a shortage occurs? Round your answers to 3 decimal places. 50,000 units: 60,000 units: 70,000 units:
Solution:
FC = Fixed Cost = $100,000
VC = Variable Cost = $34 per doll
SP1 = Sales Price (during holiday season) = $42 per doll
SP2 = Sales Price (in January – off season ) = $10 per doll
Average demand = D = Demand = 60,000 = Mean = Miu = 60,000
SD = Standard Deviation = 15,000
Demand follows normal probability distribution
Tentative Production forecast = 60,000 dolls
Calculated Production forecast = ?
Profit = Sales – (Variable Cost + Fixed Cost)
During the holiday season,
For 40,000 dolls, sales = 40,000 * 42 = $1,680,000
profit = $1,680,000 – (VC+FC)
VC = 34*40,000 = 1,360,000
FC = Fixed Cost = $100,000
TC = Total Cost = VC + FC = 1,360,000+100,000 = $1,460,000
profit = 1,680,000 – 1,460,000 = $220,000
Maximum Profit = $220,000
Average Profit:
Off season sale price * Demand = $10*40,000 = $400,000
average sales = ($400,000 + 1,680,000 ) / 2 = $1,040,000
Average profit = 1,040,000 – 73,000 = $967,000
Probability of a loss:
Probability = 1 - F(Z)
where F(Z) = (Qty – Miu / SD)
F(Z) = 60,000 - 40,000 / 15,000 = 1.33
Absolute value of (1 – F(Z)) = 0.33
Hence probability of loss = 0.33 = 1/3
Possibility of a Shortage = 1 – Probability of loss = 1 – 1/3 = 2/3
