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A manager intends to order a new machine and must now decide on the number of spare parts to order along with the machine

Economics

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A manager intends to order a new machine and must now decide on the number of spare parts to order along with the machine. The parts cost $432 each and have no salvage value. The manager has compiled the frequency distribution for the probable usage of spare parts:3 spare parts with frequency 0.13;4 spare parts with frequency 0.14;5 spare parts with frequency 0.09;6 spare parts with frequency 0.13; and 7 spare parts with frequency 0.51. For what range of shortage costs would stocking 5 spare parts constitute an optimal decision ?