Exercise $3.$ Jessica is preparing to host a fundraising event for a local animal shelter in Atlanta. As part of the event, Jessica plans to set up a booth to sell handmade crafts, including woven baskets. Jessica purchases these baskets online for $$6$ each and intends to sell them at the event for $$10$ each. If there are any baskets left unsold after the fundraiser, Jessica will donate them to the animal shelter to use as storage for pet supplies.

The demand for these baskets during the fundraiser is given by a discrete uniform distribution over the interval $101,300($meaning that the demand random variable takes each of the values $101,102,103,$dots,$300$ with equal probability$).$

a$.)$ What is the optimal newsvendor order quantity?

b$.)$ Before placing the order, Jessica discovers that she already had $90$ units in storage. What is the optimal order quantity now?

c$.)$ What would be the optimal order quantity if she instead found $190$ units in storage?