Question

The management of Brinkley Corporation is interested in using simulation to estimate the profit (in $) per unit for a new product. The selling price for the product will be $43 per unit. Probability distributions for the purchase cost, the labor cost, and the transportation cost are estimated in the following table.

ProcurementCost($) Probability LaborCost ($) Probability TransportationCost ($) Probability
10 0.25 20 0.10 3 0.75
11 0.45 22 0.25 5 0.25
12 0.30 24 0.35
25 0.30
(a)
Compute profit (in $) per unit for the base-case scenario.
$ /unit
(b)
Compute profit (in $) per unit for the worst-case scenario.
$ /unit
(c)
Compute profit (in $) per unit for the best-case scenario.
$ /unit
(d)
Construct a simulation model to estimate the mean profit (in $) per unit. (Use at least 1,000 trials. Round your answer to two decimal places.)
$
(e)
Management believes 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. (Round your answer to three decimal places.)

Answer 1

To calculate the profit per unit for different scenarios, subtract the costs from the selling price. Use simulation to estimate the mean profit per unit and the probability of the profit being less than $5.

Step-by-step explanation:

a) To calculate the profit per unit for the base-case scenario, we need to subtract the purchase cost, labor cost, and transportation cost from the selling price.

Profit per unit = Selling price - Purchase cost - Labor cost - Transportation cost

Profit per unit = $43 - $10 - $20 - $3 = $10.

b) For the worst-case scenario, we need to use the highest values for the purchase cost, labor cost, and transportation cost.

Profit per unit = $43 - $12 - $25 - $5 = $1.

c) For the best-case scenario, we need to use the lowest values for the purchase cost, labor cost, and transportation cost.

Profit per unit = $43 - $10 - $22 - $3 = $8.

d) To estimate the mean profit per unit, we can simulate the profit calculation for a large number of trials. We randomly select values from the probability distributions and calculate the profit per unit for each trial. We repeat this process for at least 1,000 trials and calculate the average of the profits per unit.

e) To estimate the probability of the profit per unit being less than $5, we can simulate the profit calculation for a large number of trials. We randomly select values from the probability distributions and calculate the profit per unit for each trial. We count the number of trials where the profit per unit is less than $5 and divide it by the total number of trials.