A manager wants to purchase a new piece of processing equipment and must decide on the number of a spare part to order with the new equipment. The spares cost $$200$ each, and any unused spares will have an expected salvage value of $$50$ each. The probability of usage of parts can be described by the following distribution:

Number $0123$

Probability $0\mathrm{.}100\mathrm{.}500\mathrm{.}250\mathrm{.}15$

If the part fails and a spare is not available, it will take two days to obtain a replacement and install it$.$ The cost for idle equipment is $$400$ per day. The spare is expected to cost the same in the future $($$$200$ per unit$).$ What quantity of spares should be stocked? use the ratio method