Question

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 $50 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	0.45	20	0.2	2	0.75
12	0.25	22	0.25	4	0.25
13	0.3	25	0.35
		27	0.2

1. Compute profit per unit for the base-case, worst-case, and best-case.
   
   Profit per unit for the base-case: $  
   
   Profit per unit for the worst-case: $  
   
   Profit per unit for the best-case: $  
   
2. Construct a simulation model to estimate the mean profit per unit. If required, round your answer to the nearest cent.
   
   Mean profit per unit = $  
   
3. Why is the simulation approach to risk analysis preferable to generating a variety of what-if scenarios?
   
   The input in the box below will not be graded, but may be reviewed and considered by your instructor.
   
   
   
4. Management believes the project may not be sustainable if the profit per unit is less than $9. Use simulation to estimate the probability the profit per unit will be less than $9. If required, round your answer to one decimal place.
   
   %

Answer 1

a)

Base-case

Procurement cost = .45*10+.25*12+.3*13 = 11.4

Labor cost = .2*20+.25*22+.35*25+.2*27 = 23.65

Transportation cost = .75*2+.25*4 = 2.5

Total cost = 11.4+23.65+2.5 = 37.55

Profit per unit = selling price - total cost = 50 - 37.55 = $ 12.45

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Worst-case

Total cost = Sum of Maximum of procurement + labor + transportation cost

= 13+27+4 = 44

Profit per unit = selling price - total cost = 50 - 44 = $ 6

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Best-case

Total cost = Sum of Minimum of procurement + labor + transportation cost

= 10+20+2 = 32

Profit per unit = selling price - total cost = 50 - 32 = $ 18

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b)

Simulation model is following:

EXCEL FORMULAS:

Mean profit per unit = $ 12.46

c) Simulation approach to risk analysis is preferable to generating a variety of what-if scenarios, because simulation gives an output which depicts real-life problem more accurately, as against generating a variety of what-if scenarios, which only limits the evaluation to a limited set of scenarios.

d) Probability calculation is already shown in the simulation model

Probability that the profit per unit will be less than $ 9 = 10.8 %

Note that mean profit per unit and probability will vary for every simulation run. So, there is no fixed answer. However, the simulation output gives an approximate estimate.