A farmer that boards horses keeps an inventory of horse feed in a silo, as pictured below

Twice a day, the farmer positions a wheelbarrow under the chute under the bottom of the silo, and turns the handle to allow feed to come out into the wheelbarrow. The farmer uses their judgement to decide when they have enough in the wheelbarrow for the horses. Studies have shown that they average 1.7 m3 per day with a standard deviation of 0.3. Further information: Horse feed costs $63 per m3 , and is ordered from the local co-op. Annual demand is 365*1.7=620.5. There is a fixed fee of $70 charged for delivery. It takes two days from when the farmer orders until the feed is delivered. The farmers accountant estimates that the cost of capital, to the farmer, is 15% per year. The farm has 2 dogs and 6 cats (two are house cats, four are barn cats), in addition to the horses. The required cycle service level is up to you please justify your choice in your answer (there is a trade-off regarding the amount of safety stock, that you should acknowledge).

The farmer currently climbs to the top and checks every Monday morning, and orders if it is below the point at which the silo narrows. (What type of inventory control system is this continuous review, periodic review, or optional replenishment?)

1. Rather than checking every Monday (but not necessarily ordering each time), the farmer will only check every P days, and will place an order every time. (a) What should P be (in days, and in weeks), in order to minimize total annual ordering plus holding costs? And, (b) the farmer is thinking of switching to lower-cost feed, how would that affect your answer (i.e. should they order more, or less often than your answer in (a)?)