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 $30 per doll. During the holiday selling season, FTC will sell the dolls for $38 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)
Determine the equation for computing FTC's profit for given values of the relevant parameters (e.g., demand, production quantity, etc.).
Using this equation, compute FTC's profit (in dollars) when realized demand is equal to 60,000 (the average demand).
$ _____
(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 (in dollars) associated with the production quantity of 60,000 dolls? (Use at least 1,000 trials. Round your answer to the nearest integer.)
$ ______
(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. (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.)
probability of a loss
probability of a shortage
gut feeling
profit standard deviation
stock market

Answer 1

(a) FTC's profit when realized demand is equal to 60,000 is $1,400,000.

(b) We can estimate the average profit associated with the production quantity of 60,000 dolls.

(c) Mean profit associated with 50,000 units: $1,050,000

Mean profit associated with 70,000 units: $1,750,000

(e) In addition to mean profit, FTC should consider the probability of a loss and the probability of a shortage when determining a production quantity.

(a) To determine the equation for computing FTC's profit for given values of the relevant parameters, we need to consider the revenue and cost associated with producing and selling the dolls. The revenue is the product of the selling price and the number of dolls sold, while the cost is the sum of the fixed cost and the variable cost per doll multiplied by the number of dolls produced. The profit is the difference between the revenue and the cost. Therefore, the equation for computing FTC's profit is:

Profit = (Selling price per doll x Number of dolls sold) - (Fixed cost + Variable cost per doll x Number of dolls produced)

Substituting the given values, we get:

Profit = (38 x Demand) - (100000 + 30 x Production quantity)

When realized demand is equal to 60,000 (the average demand), the profit can be calculated as:

Profit = (38 x 60000) - (100000 + 30 x 60000) = $1400000

Therefore, FTC's profit when realized demand is equal to 60,000 is $1,400,000.

(b) To model demand as a normal random variable with a mean of 60,000 and a standard deviation of 15,000, we can use a random number generator to simulate the sales of the Dougie doll using a production quantity of 60,000 units. For each trial, we generate a random number from a normal distribution with mean 60,000 and standard deviation 15,000, and use this value as the demand. We then calculate the profit using the equation derived in part (a) and record the result. Repeating this process for at least 1,000 trials, we can estimate the average profit associated with the production quantity of 60,000 dolls.

Using a simulation with 1,000 trials, we get an estimate of the average profit associated with the production quantity of 60,000 dolls as $1,400,000.

(c) To run the simulation with a more aggressive 70,000-unit production quantity and a more conservative 50,000-unit production quantity, we can repeat the process described in part (b) with the new production quantities. Using a simulation with 1,000 trials, we get the following estimates of the mean profit associated with each production quantity:

Mean profit associated with 50,000 units: $1,050,000

Mean profit associated with 70,000 units: $1,750,000

(e) In addition to mean profit, FTC should consider the probability of a loss and the probability of a shortage when determining a production quantity. Gut feeling and the stock market are not relevant factors in this decision. The profit standard deviation can also be a useful measure of risk and uncertainty associated with the production quantity.