1) The Evergreen Company owns acreage of shrub trees to be harvested and sold each spring. The company estimates the costs of cutting and trimming the trees to be $2.50 per tree and the company receives about $5.00 per each tree sold. Unsold tree at the end of the season is worthless and must be discarded. The following distribution represents the demand.
|
Quantity sold
|
Probability
|
|
100
|
0.05
|
|
150
|
0.10
|
|
200
|
0.10
|
|
250
|
0.20
|
|
300
|
0.25
|
|
350
|
0.15
|
|
400
|
0.10
|
|
450
|
0.05
|
a) If the company decides to cut an amount equal to the expected demand what would be the profit
b) How many trees should be cut to maximize the profit?
c) What is the expected number of lost sales at this optimum quantity?