Problem: Demand for a seasonal product is estimated to be normally distributed with a mean of 1000 and a standard deviation of 300. If demand exceeds available inventory the seller incurs a shortage cost of $7 per unit. On the other hand, if demand is below inventory, the seller incurs an overage cost of $3 per unit.

a) Under the optimal order quantity, what is the probability that demand does not exceed available inventory?

b) Is the optimal order quantity smaller or larger than the mean demand? Explain why?

c) What would the optimal order quantity be if the standard deviation of demand increased from 300 to 400? Explain the result.

d) What would the optimal order quantity be if the cost of shortage is $2 per unit instead of $7 per unit (assume standard deviation is 300)?

e) Assuming the cost of shortage is $2 per unit, what would the optimal order quantity be if the standard deviation increased from 300 to 400? Explain the result.