Need solutions for problem 2(c) only.

[No Collaboration] (410 points ) A medical clinic dispenses vaccines at a steady rate of 520 doses per month. Each order placed to the vaccine manufacturer incurs a fixed cost of $140. Each vaccine dose held in inventory incurs a holding cost of $3 per year. The lead time for an order is 15 days. The clinic plans to order the same number of doses at each order but is willing to order as many times as necessary. Initially the clinic has no vaccine and its vaccination drive starts after the first order is received. The clinic is now planning its yearly budget and wants to set aside an amount for the expenses of ordering and holding vaccines. For simplifying calculations assume that each month has exactly 30 days and an year has 360 days. (a) Calculate the optimal order quantity Q, order point r, and the minimum yearly budget amount that the clinic must set aside for vaccines. (b) Suppose each vaccine dose expires 30 days after delivery to the clinic. How much and how frequently should the clinic order under this situation? (c) Consider now a vaccine that does not expire but needs ultra cold storage until it is dispensed. Each unit of cold storage has a yearly rental cost of $100 and can store up to 50 vaccines at once. This is in addition to the basic costs mentioned above. (i). How many units of storage does the store need to rent? What is the new optimal order quantity? (ii). Unfortunately, the clinic has only set aside a budget equal to the average cost computed in part (a). Therefore, it cannot afford any additional costs for cold storage. Fortunately, the government starts a program where clinics can apply to have any one of the costs subsidized by 50% i.e., either only the fixed cost can be reduced to $70 or only the holding cost to $1.5 or only the cold storage cost to $50. Does the subsidy scheme make the optimal order costs of the clinic drop to within budget? If yes, which option should the clinic choose in the subsidy scheme and what is the new optimal order quantity