$1.$ Next week, Super Discount Airlines has a flight from New York to Los Angeles that will be booked to capacity. The airline knows from history that an average of $27$ customers $($with a standard deviation of $17)$ cancel their reservation or do not show for the flight. Revenue from a ticket on the flight is $$118.$ If the flight is overbooked, the airline has a policy of getting the customer on the next available flight and giving the person a free round$-$trip ticket on a future flight. The cost of this free round$-$trip ticket averages $$235.$ Super Discount considers the cost of flying the plane from New York to Los Angeles a sunk cost.

By how many seats should Super Discount overbook the flight?

Note: Use Excel's NORM.S$.$INV$()$ function to find the z value. Round z value to $2$ decimal places. Round your answer to the nearest whole number.

$2.$ tem X is a standard item stocked in a company's inventory of component parts. Each year the firm, on a random basis, uses about $2,700$ of item X$,$ which costs $$25$ each. Storage costs, which include insurance and cost of capital, amount to $$13$ per unit of average inventory. Every time an order is placed for more of item X$,$ it costs $$26.$

a$.$ Whenever item X is ordered, what should the order size be$?$

Note: Round your answer to the nearest whole number.

b$.$ What is the annual cost for ordering item X$?$

Note: Round your order quantity to the nearest whole number and your final answer to $2$ decimal places.

c$.$ What is the annual cost for storing item X$?$

Note: Round your order quantity to the nearest whole number and your final answer to $2$ decimal places.