Phoenix Motors wants to lock in the cost of $10,000$ ounces of platinum to be used in next quarter's production of catalytic converters. It

buys $3-$month futures contracts for $10,000$ ounces at a price of $$960$ per ounce.

a$.$ Suppose the spot price of platinum falls to $$830$ in $3$ months' time. Does Phoenix have a profit or loss on the futures contract?

b$-1.$ Has it locked in the cost of purchasing the platinum it needs?

b$-2.$ What is the total lock$-$in cost$?$

c$.$ If the spot price of platinum increases to $$1,030$ after $3$ months, does Phoenix have a profit or loss on the futures contract?

d$.$ What is the total lock$-$in cost$?$