Question

In the daily production of a certain kind of rope, the number of defects per foot Y is assumed to have a Poisson distribution with ? = 2. The company is considering one of two profit models as described in parts a) and b).

a) If the profit per foot when the rope is sold is defined as ? = 50 − 2? − ?2, find the expected profit per foot.

b) If the profit per foot when the rope is sold is defined as ? = 50 − 3?, find the expected profit per foot and standard deviation of profit per foot.

c) The standard deviation of profit per foot for the model presented in a) can be shown to be $7.616 (you do not have to show this). Based on this and your findings in parts a) and b) comment on which profit model you would recommend to the company and why.

Answer 1