Question

Problem 16-11 (Algorithmic)

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.

1. Create a what-if spreadsheet model using a formula 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)?
   
   $  
   
2. 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.
   
   $  
   
   How does this compare to the profit corresponding to the average demand (as computed in part (a))?
   
   Average profit is   the profit corresponding to average demand.
   
3. 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: $  
   
4. In addition to mean profit, what other factors should FTC consider in determining a production quantity?
   
   The input in the box below will not be graded, but may be reviewed and considered by your instructor.
   
   
   
   Compare the three production quantities (50,000, 60,000, and 70,000) using all these factors. What trade-offs occur? Round your answers to 3 decimal places.
   
   50,000 units:
   
   60,000 units:
   
   70,000 units:
   
   What is your recommendation?
   
   The input in the box below will not be graded, but may be reviewed and considered by your instructor.
   

Answer 1

As it is a simulation problem the answers will vary every time simulation is run.

a) What-If spreadsheet model is following:

EXCEL FORMULAS:

What-if spreadsheet model
Fixed Cost	100000
Variable Cost	34
Selling price	42
Salvage price	10
Demand
Average	60000
Standard deviation	15000
Production Quantity	60000
Demand	60000
Sales	=MIN(B11:B12)
Revenue from Sales	=B13*B5
Amount of surplus	=B11-B13
Revenue from sales of surplus	=B15*B6
Total cost	=B3+B11*B4
Net profit	=B14+B16-B17

Profit = $ 380,000

b) Simulation model is following:

EXCEL FORMULAS:

Simulation model
Trial	Demand	Sales	Surplus	Total Revenue	Total Cost	Net Profit
1	=ROUND(NORMINV(RAND(),$B$8,$B$9),0)	=MIN(E3,$B$11)	=$B$11-F3	=F3*$B$5+G3*$B$6	=$B$3+$B$11*$B$4	=H3-I3		Average profit	=AVERAGE(J3:J502)
2	=ROUND(NORMINV(RAND(),$B$8,$B$9),0)	=MIN(E4,$B$11)	=$B$11-F4	=F4*$B$5+G4*$B$6	=$B$3+$B$11*$B$4	=H4-I4
3	=ROUND(NORMINV(RAND(),$B$8,$B$9),0)	=MIN(E5,$B$11)	=$B$11-F5	=F5*$B$5+G5*$B$6	=$B$3+$B$11*$B$4	=H5-I5
4	=ROUND(NORMINV(RAND(),$B$8,$B$9),0)	=MIN(E6,$B$11)	=$B$11-F6	=F6*$B$5+G6*$B$6	=$B$3+$B$11*$B$4	=H6-I6
5	=ROUND(NORMINV(RAND(),$B$8,$B$9),0)	=MIN(E7,$B$11)	=$B$11-F7	=F7*$B$5+G7*$B$6	=$B$3+$B$11*$B$4	=H7-I7
6	=ROUND(NORMINV(RAND(),$B$8,$B$9),0)	=MIN(E8,$B$11)	=$B$11-F8	=F8*$B$5+G8*$B$6	=$B$3+$B$11*$B$4	=H8-I8
7	=ROUND(NORMINV(RAND(),$B$8,$B$9),0)	=MIN(E9,$B$11)	=$B$11-F9	=F9*$B$5+G9*$B$6	=$B$3+$B$11*$B$4	=H9-I9
8	=ROUND(NORMINV(RAND(),$B$8,$B$9),0)	=MIN(E10,$B$11)	=$B$11-F10	=F10*$B$5+G10*$B$6	=$B$3+$B$11*$B$4	=H10-I10
9	=ROUND(NORMINV(RAND(),$B$8,$B$9),0)	=MIN(E11,$B$11)	=$B$11-F11	=F11*$B$5+G11*$B$6	=$B$3+$B$11*$B$4	=H11-I11
10	=ROUND(NORMINV(RAND(),$B$8,$B$9),0)	=MIN(E12,$B$11)	=$B$11-F12	=F12*$B$5+G12*$B$6	=$B$3+$B$11*$B$4	=H12-I12
11	=ROUND(NORMINV(RAND(),$B$8,$B$9),0)	=MIN(E13,$B$11)	=$B$11-F13	=F13*$B$5+G13*$B$6	=$B$3+$B$11*$B$4	=H13-I13
12	=ROUND(NORMINV(RAND(),$B$8,$B$9),0)	=MIN(E14,$B$11)	=$B$11-F14	=F14*$B$5+G14*$B$6	=$B$3+$B$11*$B$4	=H14-I14
13	=ROUND(NORMINV(RAND(),$B$8,$B$9),0)	=MIN(E15,$B$11)	=$B$11-F15	=F15*$B$5+G15*$B$6	=$B$3+$B$11*$B$4	=H15-I15
14	=ROUND(NORMINV(RAND(),$B$8,$B$9),0)	=MIN(E16,$B$11)	=$B$11-F16	=F16*$B$5+G16*$B$6	=$B$3+$B$11*$B$4	=H16-I16
15	=ROUND(NORMINV(RAND(),$B$8,$B$9),0)	=MIN(E17,$B$11)	=$B$11-F17	=F17*$B$5+G17*$B$6	=$B$3+$B$11*$B$4	=H17-I17
16	=ROUND(NORMINV(RAND(),$B$8,$B$9),0)	=MIN(E18,$B$11)	=$B$11-F18	=F18*$B$5+G18*$B$6	=$B$3+$B$11*$B$4	=H18-I18
17	=ROUND(NORMINV(RAND(),$B$8,$B$9),0)	=MIN(E19,$B$11)	=$B$11-F19	=F19*$B$5+G19*$B$6	=$B$3+$B$11*$B$4	=H19-I19
18	=ROUND(NORMINV(RAND(),$B$8,$B$9),0)	=MIN(E20,$B$11)	=$B$11-F20	=F20*$B$5+G20*$B$6	=$B$3+$B$11*$B$4	=H20-I20
19	=ROUND(NORMINV(RAND(),$B$8,$B$9),0)	=MIN(E21,$B$11)	=$B$11-F21	=F21*$B$5+G21*$B$6	=$B$3+$B$11*$B$4	=H21-I21
20	=ROUND(NORMINV(RAND(),$B$8,$B$9),0)	=MIN(E22,$B$11)	=$B$11-F22	=F22*$B$5+G22*$B$6	=$B$3+$B$11*$B$4	=H22-I22
21	=ROUND(NORMINV(RAND(),$B$8,$B$9),0)	=MIN(E23,$B$11)	=$B$11-F23	=F23*$B$5+G23*$B$6	=$B$3+$B$11*$B$4	=H23-I23
22	=ROUND(NORMINV(RAND(),$B$8,$B$9),0)	=MIN(E24,$B$11)	=$B$11-F24	=F24*$B$5+G24*$B$6	=$B$3+$B$11*$B$4	=H24-I24
23	=ROUND(NORMINV(RAND(),$B$8,$B$9),0)	=MIN(E25,$B$11)	=$B$11-F25	=F25*$B$5+G25*$B$6	=$B$3+$B$11*$B$4	=H25-I25
24	=ROUND(NORMINV(RAND(),$B$8,$B$9),0)	=MIN(E26,$B$11)	=$B$11-F26	=F26*$B$5+G26*$B$6	=$B$3+$B$11*$B$4	=H26-I26

Average profit based on 500 simulation trials = $ 187,807

Average profit is less than the average corresponding to average demand (in part a) .

c)

Change the production quantity in cell B11 , to 70000 and 50000 units.

And note the average profit in cell M3

Average profit for:

50,000-unit product quantity = $ 212,723

70,000-unit product quantity = $ 65,025

d) The other factors that should be considered are risks such as probability of loss, probability of shortage

An additional column is added to the simulation model to determine probability of shortage

Shortage = Demand - Sales

EXCEL FORMULA

for column K: K3 =E3-F3 copy down to row 502

to calculate probability of shortage: N6 =COUNTIF(K3:K502,">"&0)/500

Probability that a shortage occurs for:

50,000 units: 0.758

60,000 units: 0.544

70,000 units: 0.268

Profit associated with production level of 50,000 units is higher. Therefore, it is recommended to produce 50,000 units