Please explain step by step and provide formulas for the below:

The catering manager of La Vista Hotel, Lisa Ferguson, is disturbed by the amount of silverware she is losing every week. Last Friday night, when her crew tried to set up for a banquet for 500 people, they did not have enough knives. She decides she needs to order some more silverware, but wants to take advantage of any quantity discounts her vendor will offer. For a small order (2,000 or fewer pieces), her vendor quotes a price of $1.80/piece. If she orders 2,0015,000 pieces, the price drops to $1.60/piece. 5,00110,000 pieces brings the price to $1.40/piece, and 10,001 and above reduces the price to $1.25. Lisas order costs are $200 per order, her annual holding costs are 5%, and the monthly demand is 3750 pieces. For the best option:

a. What is the optimal order quantity given the discount levels?

b. What is the annual holding cost at the optimal quantity?

c. What is the total annual cost, including ordering, holding, and purchasing the silverware?