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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

0.3

$16,000

0.35

$18,000

0.2