Anvils Works' requires, on average, $2,600$ tons of aluminum each week, with a standard deviation of $800$ tons. The lead time to receive its orders is $11$ weeks. The holding cost for one ton of aluminum for one week is $$9.$ It operates with a $0\mathrm{.}99$ in$-$stock probability.

On average, how many tons does it have on order?

On average, how many tons does it have on hand?

If its average inventory was $7,500$ tons, what would be its average holding cost per week?

If its average inventory was $10,000$ tons, what would be its average holding cost per ton of aluminum?

Suppose its on$-$hand inventory is $5,000$ tons, on average. What instock probability does it offer to its customers?