quantities and the corresponding cost.

OR

V$.($a$)$ A company is making a large boiler installation. A certain automatic monitoring unit is crucial for the operation of the whole system. The original spares for this unit can be purchased for $2,000$ each. The probability distribution for failures of this unit during the life time of the installation is known to be

$\backslash$table$[[$Demand:$,0,1,2,3,4],[$Probability:$,0\mathrm{.}30,0\mathrm{.}25,0\mathrm{.}25,0\mathrm{.}10,0\mathrm{.}10]]$

If a spare is needed and is not available, the total cost to the company in down time and replacement cost will be $15,000.$ Unused spares have no salvage value. Formulate Total cost matrix and determine the optimum number of spares to stock.