A manager is going to purchase new processing equipment and must decide on the number of spare parts 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 can be described by this distribution:

Number $0123$

Probability $\mathrm{.}10\mathrm{.}50\mathrm{.}25\mathrm{.}15$

If a part fails and a spare is not available, two days will be needed to obtain a replacement and install it$.$ The cost for idle equipment is $$500$ per day. What quantity of spares should be ordered?

a$.$ Use the ratio method. $($Round your answer to $2$ decimal places.$)$

Service level is $\_\_\_,$ so we need to order $\_\_\_$ spares.

b$.$ Use the tabular method.

$\_\_\_$ spares

Solution