An industrial psychologist conducts two efficiency studies at the Chilco appliance factory. The first study indicates that the average worker who arrives on the job at 8:00 A.M. will have assembled -' + 61² + 13t blenders in 1 hours (without a break), for 0 < t < 4. The second study suggests that after a 15-minute coffee break, the average worker can assemble -/ +/ + 251 blenders in 1 hours after the break for 0 < t < 4. Note: The 15-minute break is not part of the work time. a. Verify that if the coffee break occurs at 10:00 A.M., the av- erage worker will assemble 42 blenders before the break and 49 blenders for the two hours after the break. b. Suppose the coffee break is scheduled to begin x hours af- ter 8:00 A.M. Find an expression for the total number of blenders N(x) assembled by the average worker during the morning shift (8 A.M. to 12:15 P.M.). c. At what time should the coffee break be scheduled so that the average worker will produce the maximum number of blenders during the morning shift? How is this optimum time related to the point of diminishing returns?

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