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 $$172$ each, and any unused spares will have an expected salvage value of $$42$ each. The probability of usage can be described by this distribution:

$\backslash$table$[[$Number$,0,1,2,3],[$Probability$,15,\mathrm{.}60,\mathrm{.}20,\mathrm{.}05],[$Click here for the Excel Data File,,,,$]]$

If a part fails and a spare is not available, $2$ days will be needed to obtain a replacement and install it$.$ The cost for idle equipment is $$570$ per day. What quantity of spares should be ordered?

a$.$ Use the ratio method.

Note: Round the SL answer to $2$ decimal places and the number of spares to the nearest whole number.

b$.$ Use the tabular method and determine the expected cost for the number of spares recommended. Note: Do not round intermediate calculations. Round your final answer to $2$ decimals.

Expected cost is $$