Sarah$$s Organic Soap Company makes organic liquid soap. One of the raw materials for her soaps is organic palm oil. She needs $1000$ kg of palm oil per day, on average. The supplier charges a $$60$ delivery fee per order $($which is independent of the order size$)$ and $$4\mathrm{.}75$ per kg$.$ Sarah$$s annual holding cost is $25$ percent. Assume she operates and sells $5$ days per week, $52$ weeks per year.

a$.$ If Sarah wants to minimize her annual ordering and inventory holding costs, how much palm oil should she purchase with each order $($in kilograms$)?$

b$.$ If Sarah orders $4000$ kg with each order, what would be the annual sum of the ordering and holding costs?

c$.$ If Sarah orders $8000$ kg with each order, what would be the sum of the ordering and holding costs per kilogram sold