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 $484 each and have no salvage value. The manager has compiled the frequency distribution for the probable usage of spare parts:9 spare parts with frequency 0.05;10 spare parts with frequency 0.14;11 spare parts with frequency 0.22;12 spare parts with frequency 0.16; and 13 spare parts with frequency 0.43. For what range of shortage costs would stocking 11 spare parts constitute an optimal decision ?

a. Between 170.3and 504.5

b. Between 56.77and 168.2

c. Between 136.2and 403.6

d. Between 113.5and 336.3