In: Statistics and Probability
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 uncertain. The normal probability distribution with an average of 60,000 dolls and a standard deviation of 15,000 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) Create a what-if spreadsheet model using formulas that relate the values of production quantity, demand, sales, revenue from sales, amount of surplus, revenue from sales of surplus, total cost, and net profit. What is the profit when demand is equal to its average (60,000 units)? $ 380000 (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 in whole dollar. $ 192014 How does this compare to the profit corresponding to the average demand (as computed in part a)? The input in the box below will not be graded, but may be reviewed and considered by your instructor. In a perfect world, profit will be maximized when supply and demand intersect. (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 average profit associated with each? Round your answer in whole dollar. When ordering 50,000 units, the average profit is approximately $ 224676 When ordering 70,000 units, the average profit is approximately $ 45547 (d) Besides average 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. Round your answer in whole dollar. Production Quantity Average Net Profit Profit Standard Deviation Maximum Net Profit Probability of a Loss Probability of a Shortage 40,000 $ $ $ 50,000 $ $ $ 60,000 $ $ $ 70,000 $ $ $ What is your recommendation?
ANSWER :-
In planning for the forthcoming Christmas season,
Fresh Toy Company (FTC) structured another doll considered The Dougie that shows youngsters how to move. The fixed expense to create the doll is $100,000.
The variable cost, which incorporates material, work, and sending costs, is $34 per doll. During the occasion selling season, FTC will sell the dolls for $42 each.
In the event that FTC overproduces the dolls, the overabundance dolls will be sold in January through a merchant who has consented to pay FTC $10 per doll.
Interest for new toys during the occasion selling season is questionable. The typical likelihood dispersion with a normal of 60,000 dolls and a standard deviation of 15,000 is thought to be a decent depiction of the interest.
FTC has probably chosen to create 60,000 units (equivalent to average interest), however it needs to direct an investigation with respect to this generation amount before settling the choice. (a) Create an imagine a scenario where spreadsheet model utilizing recipes that relate the estimations of generation amount, request, deals, income from deals, measure of overflow, income from offers of excess, complete expense, and net benefit.
What is the benefit when request is equivalent to its normal (60,000 units)?
$ 380000
(b) Modeling request as a typical arbitrary variable with a mean of 60,000 and a standard deviation of 15,000, mimic the offers of The Dougie doll utilizing a generation amount of 60,000 units. What is the gauge of the normal benefit related with the generation amount of 60,000 dolls? Round your answer in entire dollar. $ 192014 How does this contrast with the benefit comparing to the normal interest (as figured to some degree a)? The contribution to the case beneath won't be evaluated, yet might be checked on and considered by your teacher. Ideally, benefit will be amplified when free market activity meet. (c) Before settling on an official conclusion on the generation amount, the board needs an examination of an increasingly forceful 70,000-unit creation amount and a progressively preservationist 50,000-unit generation amount. Run your reproduction with these two generation amounts. What is the normal benefit related with each? Round your answer in entire dollar. When requesting 50,000 units, the normal benefit is around $ 224676 When requesting 70,000 units, the normal benefit is roughly $ 45547 (d) Besides normal benefit, what different variables should FTC consider in deciding a generation amount? Look at the four generation amounts (40,000; 50,000; 60,000; and 70,000) utilizing every one of these elements. What exchange offs happen? Whenever required, round Probability of a Loss to three decimal spots and Probability of a Shortage to two decimal spots. Round your answer in entire dollar. Generation Quantity Average Net Profit Standard Deviation Maximum Net Profit Probability of a Loss Probability of a Shortage 40,000 $ 50,000 $ 60,000 $ 70,000
I only recommend the Production Quantity Average Net Profit Profit Standard Deviation Maximum Net Profit Probability of a Loss Probability of a Shortage.