Problem $12-41($Algo$)$

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 $$171$ each, and any unused spares will have an expected salvage value of $$41$ each. The probability of usage can be described by this distribution:

$\backslash$table$[[$Number$,0,1,2,3],[$Probability$,\mathrm{.}10,\mathrm{.}50,\mathrm{.}25,\mathrm{.}15]]$

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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 $$560$ per day. What quantity of spare's should be ordered?

a$.$ Use the ratio method. $($Round the SL answer to $2$ decimal places and the number of spares to the nearest whole number.$)$

Answer is complete but not entirely correct.

$,$ so we need to order

Spares.

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

Answer is complete but not entirely correct.

Expected cost is

$ $472\mathrm{.}65x$