Please show work for questions within both sections: Continuous (Q 1-3) and Discrete (Q1) . Much appreciated! Newsvendor Model Assignment

Continuous:

Q1. For a moment forget the newsvendor model. You are faced with the same problem of deciding optimal order quantity. Let the expected demand you face be M. Let your cost of overage (unsold stock) be higher than your cost of underage (lost sales). Purely based on your intuition, do you choose to order more/less than the mean?

Q2. Consider the Newsvendor model: Let the Cost of Overage (Co) = $0.50 Let the Cost of Underage (Cu) = $1.50 Let Demand (D) be normally distributed with mean = 80 and standard deviation = 12 What is the optimal order quantity (Q*)? (Note: Round up solution to nearest integer)

Q3. Consider the Newsvendor model: Let the Cost of Overage (Co) = $0.50 Let the Cost of Underage (Cu) = $2.00 Let Demand (D) be normally distributed with mean = 100 and standard deviation = 15 a) What is the optimal order quantity Q*? b) What would the new order quantity (Q') be if the Cost of Underage Cu is $1.50 instead? Note the effect of the decrease in Cu on the optimal order quantity. (Note: Round up solution to nearest integer)

Discrete:

Q1. The Power at Ice Station Lion is supplied via solar cells. Once a year, a plane flies in and sells solar cells at a price of $20 per cell. Because of uncertainty about future power needs, the ice station can only guess the number of cells that will be required during the coming year:

No. of Cells	Probabillity
50	0.20
60	0.15
70	0.30
80	0.10
90	0.15
100	0.10

If the ice station runs out of solar cells, a special order must be placed at a cost of $30 per cell. How many cells should be ordered from the plane to minimize expected cost?