B&H needs to decide how to manage its inventory of cameras. The demand for cameras at B&H is $200$ cameras per week. Each time that B&H places an order for a new shipment of cameras, it must pay $$80$ in fixed processing fees. A camera costs B&H $$60$ to purchase. The cost for B&H to hold a camera in its store for one week is $$4.$ Assume that the lead time for the delivery of a camera is $0$ weeks.

Suppose that B&H places orders for cameras in quantities of $50$ cameras at a time and places a new order for cameras each time that it runs out. Draw a graph showing the number of cameras that B&H has on$-$hand in inventory at each point in time up until the time when it places its fourth order. Label the points in time at which B&H places a new order. Assume that B&H places its first order for $50$ cameras on day $0.$

Suppose again that B&H places orders for $50$ cameras at a time. What will be B&H$$s average holding costs per week? What will be B&H$$s average fixed ordering costs per week?

What is the optimal number of cameras for B&H to order each time that it places an order? Assuming that B&H orders according to its optimal ordering quantity $($EOQ$),$ what will be B&H$$s average fixed ordering costs over the course of a week? What will be B&H$$s average holding costs over the course of a week?

Suppose now that the lead time for the delivery of a shipment of cameras increases to $0\mathrm{.}2$ week. Assuming that B&H orders according to its optimal order quantity from part c above, what should be B&H$$s reorder point for a shipment of cameras?

Suppose that the lead time for the delivery of cameras is still $0\mathrm{.}2$ week. However, rather than placing an order when B&H$$s inventory of cameras reaches its reorder point calculated in part d above, B&H decides to place a new order for cameras whenever it has $60$ cameras in inventory. How much additional holding costs $($over the EOQ holding costs$)$ will B&H incur as a result of this ordering policy? $($Suppose that B&H orders according to the EOQ level each time that it places an order.$)$

$[$Extra Credit$]$ Suppose now that the lead time for the delivery of a shipment of cameras increases to $0\mathrm{.}5$ week. Assuming that B&H orders according to its optimal order quantity from part c above, what should be B&H$$s reorder point for a shipment of cameras? Explain carefully your answer.