Tango’s Kiosk needs to decide how many pretzels to order for Spring Carnival. The pretzels cost $0.10 each and sell for $0.25 each; unsold pretzels can be returned to the supplier for a $0.05 each refund (the supplier then sells them in its Day Old Shopper for $0.08 each). Demand is estimated to be normal with a mean of 500 and standard deviation of 100.
a. How many pretzels should they order?
b. Suppose demand has standard deviation of 200. How many pretzels should be ordered now? What can you say about the relationship between order quantity and demand uncertainty (standard deviation)?
c. Due to a surge in pretzel demand, the cost per pretzel to Tango’s Kiosk goes up to $0.18; however, due to the extreme price-elasticity of students, they can still only sell them for $0.25. Unsold pretzels still only fetch $0.05 upon return. Determine how many pretzels Tango’s Kiosk should order when the standard deviation of demand is 100 and when the standard deviation of demand is 200. What do you note about the relationship between order quantity and demand uncertainty? Discuss why the relationship differs from (b).
d. Suppose Tango’s Kiosk decides to set the probability of a stock-out at 10% (i.e., the probability that total demand exceeds the order quantity is 10%) due to the competition. How many pretzels should be ordered if standard deviation of demand is 200?