A refinery in Houston replaces all of the 3" full-open ball valves in its facility according to a very strict maintenance policy which spaces replacements fairly uniformly throughout the year. The refinery has approximately 1000 of these valves in place and safety regulations call for annual replacement. Ball valves are priced according to the schedule below. It costs $30 to place an order for valves and spare parts carrying costs are estimated at $7 per valve per year.
AMOUNT PRICE
1 to 75 $22.50
76 to 119 20.00
120 + 18.25
What order quantity will enable the refinery to achieve the lowest total cost for the year in purchasing the 3" ball valves?