A grocery store needs to decide in September how many turkeys to order for the Thanksgiving holiday. These premium turkeys are sold for $$34\mathrm{.}99$ and cost $$12\mathrm{.}25$ each. Because these turkeys are prepared only for the holiday season, the store managers consider unsold Turkeys after Thanksgiving a total loss. The managers are uncertain of the demand. Nevertheless, they believe a $1-$in$-10$ chance that demand will be greater than $1000,$ top at $1200,$ and a $1-$in$-10$ chance that demand will be less than $600.$ The demand is just as likely to be greater than $800$ as less than $800.$

a$.$ Help the managers identify the demand distribution $[$ensure you use all the information we had when running the fitting procedure and explain$].$ What theoretical distribution and its

parameters do you think works best?

b$.$ Assume that their managers have a strong feeling that demand is in a beta distribution. In addition, the order quantity can only be in the $100$s because of the agreement with the

vendor. Build a simulation model and suggest an order quantity with proper explanations.

c$.$ What happens if they can sell unsold turkeys at a deep discount $($$$10$ each after Thanksgiving$)?$ How does this affect the ordering quantity decision?