The Fraser Valley Soap company in British Columbia produces natural organic soaps. The company needs to purchase organic palm oil to make the natural soaps. The supplier of organic palm oil charges $35 per order (independent of the order size) in addition to the material cost of $1.20 per kg ordered. The company uses 5,000 kg of palm oil per week on average. The annual holding cost per unit is 35% of the material cost per unit. Assume 52 weeks per year.

a) Suppose the company ordered 3,800 kg each time they placed an order for palm oil. How many orders per year would they place on average? 

b) If the company wants to minimize the sum of holding and ordering costs, how much palm oil should it purchase with each order (in kg)? 

c) If the company places an order for 15,000 kg or more, then the supplier of palm oil will provide them with a 4% discount off the regular material cost of $1.20 per kg. If they did this with each order, what would be their average weekly total cost (in $)? 

Note: For part c), include the purchasing, holding and ordering costs.