Question

In preparing for the 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 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 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 demand. FTC has tentatively decided to produce 60,000 units, but it wants to conduct an analysis regarding this production quantity before finalizing the decision.
a) Create a what-if spreadsheet model using the 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 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? How does this compare to the profit corresponding to the average demand (as computed in part a)?
c) Before making a final decision on the production quantity, management wants an analysis of more agressive 70,000 unit production quantity and a more conservative 50,000 unit production quanty. Run the simulation with these two production quantities. (Use Excel Analytical Problem Solver)

Answer 1

Answer and Explanation:

FC = Fixed Cost = $100,000

VC = Variable Cost = $34 per doll

SP1 = Sales Price (during holiday season) = $42 per doll

SP2 = Sales Price ( January – off season ) = $10 per doll

Average demand :

Demand = 60,000

Mean = 60,000

Standard Deviation = 15,000

Demand follows normal probability distribution

Tentative Production forecast = 60,000 dolls

Calculated Production forecast =

Average Profit:

Profit standard Deviation:

Maximum Profit:

Profit = Sales – (Variable Cost + Fixed Cost)

During the holiday season,

For 40,000 dolls

Soales = 40,000 * 42 = $1,680,000

próofit = $1,680,000 – (VC+FC)

VC = 34*40,000 = 1,360,000

FC = Fixed Cost = $100,000

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

=$2,080,000/2

= $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

=20,000/15,000

= 1.33

Absolute value of (1 – F(Z)

= 0.33

Probability of loss = 0.33 or 1/3

Possibility of a Shortage = 1 – Probability of loss = 1 – 1/3 = 2/3