Given a uniform demand distribution in the range $100,130,$ the sale price per unit is $$16,$ the cost

per unit is $$12,$ and the salvage value per unit is $$2.$ If a contract is signed with the supplier, the

cost per unit will be reduced to $$10,$ and unsold units can be bought back at $$6$ per unit. The

probability density function for the demand is $f(x)=\frac{1}{b-a}.$

a$)$ Calculate the expected cost and write down the expected cost function.

b$)$ Determine the optimal order quantity $Q^{**}.$

c$)$ What is the percentile of the demand at the optimal order quantity $Q^{**}?$

PLEASE ANSWER DETAILED, ESPECCIALY DERIVATIVE PARTS.