Question $2$: Ford and GM carry spare parts for their dealers at a third$-$party warehouse in Michigan's Upper Peninsula. Demand for Ford spare parts is $1500$ units per year, whereas demand for GM parts is $1600$ per year. Each spare part's price is $$100$ and both companies have annual holding costs of $10$ percent of this price. Currently, each company uses a separate truck to ship these parts. Each truck has a fixed cost of $$500.$a$)$ What is the optimal order size for Ford and for GM$?$ What is the total cost $($the annual ordering cost and the annual holding cost only$)$ for each company?b$)$ A third$-$party logistics provider has offered to combine shipments for each of the two companies on a single truck. This will increase the cost of each truck to $$800.$ Should Ford and GM accept the third party's proposal $($considering the total annual cost of ordering and holding only$)?$