Question

Problem 14-1 (All answers were generated using 1,000 trials and native Excel functionality.) The management of Brinkley Corporation is interested in using simulation to estimate the profit per unit for a new product. The selling price for the product will be $45 per unit. Probability distributions for the purchase cost, the labor cost, and the transportation cost are estimated as follows:

Procurement Cost ($)	Probability	Labor Cost ($)	Probability	Transportation Cost ($)	Probability
10	0.2	18	0.25	2	0.74
12	0.45	20	0.1	5	0.26
13	0.35	22	0.35
		25	0.3

(a) Compute profit per unit for base-case, worst-case, and best-case.

Profit per unit for base-case:$

Profit per unit for worst-case: $

   Profit per unit for best-case: $

(b) Construct a simulation model to estimate the mean profit per unit. If required, round your answer to the nearest cent.

   Mean profit per unit = $

(c) Why is the simulation approach to risk analysis preferable to generating a variety of what-if scenarios?

(d) Management believes that the project may not be sustainable if the profit per unit is less than $5. Use simulation to estimate the probability the profit per unit will be less than $5. If required, round your answer to a one decimal digit percentage. %

Answer 1

answer a

Profit = Selling Price - Purchase Cost - Labor Cost - Transportation Cost

Base case = 45 - 12 - 22 - 2 => $ 9 / unit

worst case = 45 - 13 - 25 - 5 => $ 2 / unit

best case = 45 - 11 -18 - 2 => $ 14 / unit

	Base-case	Worst-case	Best-case
(highest probability)	(Highest value)	(lowest value)
Unit Revenue	45	45	45
Procurement Cost	12	13	11
Labor cost	22	25	18
Transportation Cost	2	5	2
Unit Profit	9	2	14

b)

Purchase Cost	Interval	Labour Cost	Interval	Transportation Cost	Interval
10	0-19	18	0-24	2	0-73
12	20-64	20	25 - 34	5	74-100
13	65-100	22	35- 69
	25	25	70-100

Mean of purchase cost = 10+12 +13/3 = 11.66

Mean of labor cost =18+ 20 + 22 + 25 / 4 = 21,25

Mean of transportation cost = 7/2 = 3.5

Profit = 45 - 11.66 - 21.25 - 3.5 = $8.59/unit

based on simulation model mean = $8.59/unit

answer c

Simulation approach to risk analysis preferable to generating a variety of what-if scenarios because a what- if Analysis involves generating values for the probabilistic inputs ( direct labour cost, parts cost, and first year demand and comtputing the resulting value for the profit. It is a trial and error approach to learning about th erange of possible outputs for a model. Trial values are choosen for the model input an dthe value of outputs i scomputed.

answer d

Simulation will provide a distribution of the profit per unit values. Calculating the percentage of simulation trials providing a profit less than $5 per unit would provide an estimate of the probability the profit per unit will be unacceptably low.

if purchase cost labour cost and transporattion cost will be 12, 13 or 22, 25 or 5 respectively and in these cases profit will be less than 5