Operations research, management homework help

Please show all steps with explanation.

Question:

A pizza restaurant that orders cheese from a global mozzarella cheese
manufacturer is considering two different transportation carriers for its (in-bound) shipments
of this “raw material.” The pizza restaurant uses 1 lb of mozzarella cheese per pizza. Average
demand for pizzas at the restaurant is 100 per day (so, average demand for cheese is 100
lbs/day). The restaurant estimates that the sD for pizza demand is 5 pizzas per day (so the sD
for cheese required is 5 lbs/day). The materials cost for the cheese is \$2/lb. Holding costs
for inventory in the restaurant is 0.50 per year (h), and for in-transit inventory (i), 0.25. The
carriers provide the following schedule to the restaurant:
Performance Carrier 1 Carrier 2
Minimum shipment, lbs 1,000 1,250
Transit time, average 2 days 1 day
Order processing time 1 day 1 day
Lead time 3 days 2 days
s.d. of lead time, sL 0.5 day 1 day
Shipment cost, \$/lb 0.25 0.275
a) How much safety inventory of mozzarella cheese will the pizza restaurant need to hold
under each of these two carrier options? Show how you calculated this SI value.
b) If the company orders the minimum shipment amount each time it orders, what is the intransit
inventory cost if the mozzarella manufacturer uses FOB Origin, Freight Collect for
shipment?
c) Which carrier should the pizza restaurant contract with if it wants to minimize the total
costs associated with purchasing the cheese? Show why you make this recommendation