GM is trying to decide whether to introduce a new car model. The selling price f
ID: 451384 • Letter: G
Question
GM is trying to decide whether to introduce a new car model. The selling price for the car will be $27,000.
The fixed cost of developing the car is assumed to be uniformly distributed between $500 million and $1 billion.
The demand for the car is described by a normal distribution with a mean of 120,000 units and a standard deviation of 30,000.
The unit variable cost for the car is distributed as shown on the right.
(a) Simulate the profit with 1000 trials. What is the mean profit from the simulation?
(b) GM is willing to introduce the car if there is at least 95% probability of making a profit and at least 90% probability of making profit of at least $100 million. Compute these two probabilities and make a recommendation.
Cost per Unit
Probability
$12,000
0.15
$14,000
0.30
$16,000
0.35
$18,000
0.20
Cost per Unit
Probability
$12,000
0.15
$14,000
0.30
$16,000
0.35
$18,000
0.20
Explanation / Answer
Answer: Selling price = $27,000 Fixed cost is between: $500 million $1,000 million Cost per Unit Probability cost Fixed cost mean = $750 million $12,000 0.15 $1,800 Standard deviation = 353.5533906 $14,000 0.3 $4,200 $16,000 0.35 $5,600 Z-value = -0.70711 $18,000 0.2 $3,600 Therefore probability = 0.23975 Mean variable cost = $15,200 Hence the fixed cost = $880.12 Also demand: Mean units = 120000 units standard deviation = 30000 Z value = 4 Probaility = 0.999968329 So the profit = $1,415,896,505.05
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