Anvil's Works requires on average 2,800 tons of aluminum each week with a standard deviation of 1,000 tons. The lead time to receive their orders is 10 weeks. The holding cost for 1 ton of aluminum for one week is $11. They operate with a 0.98 in-stock probability.

a) on average how many tons do they have on order?
b) on average how many tons do they have on hand?
c) if their average inventory were 5000 tons, what their average holding cost per week?
d) if their average inventory were 10,000 tons, what their average holding cost per ton of aluminum demanded each week?
e) suppose their on-hand inventory is 4975 tons on a average. what in-stock probability do they offer to their customers?