Maximizing Profit on Ice Skates A factory manufacturestwo kinds of ice skates: racing skates and figure skates.The racing skates require 6 work-hours in the fabricationdepartment, whereas the figure skates require 4 work-hoursthere. The racing skates require 1 work-hour in the finishing department, whereas the figure skates require 2 work-hours there. The fabricating department has available at most 120 work-hours per day, and the finishing department has no more than 40 work-hours per day available. If the profit on each racing skate is $10 and the profit on each figure skate is $12, how many of each should be manufactured each day to maximize profit? (Assume that all skates made are sold.)

Packages arrive at the stockroom and are delivered on carts to offices and laboratories by student employees. The carts and packages are various sizes and shapes. The students are paid according to the carts used. There are 6 carts and the pay for their use is Product C1: $1 Product C2: $3 Product C3: $2 Product C4: $4 Product C5: $1 Product C6: $2 On a particular day, 9 packages arrive, and they can be delivered using the 6 carts as follows: C1 can be used for packages P1, P3, P4 and p7. C2 can be used for packages P2, P5, and P6, and p8. C3 can be used for packages P1, P2, P5, P6, and P7. C4 can be used for packages P3, P6, and P7 and 9. C5 can be used for packages P2, P4 and p8. C6 can be used for packages P1, P2 and P3 The stockroom manager wants the packages delivered at minimum cost. Using minimization techniques described in this unit, present a systematic procedure for finding the minimum cost solution. Use Petrik Method

The Fore and Aft Marina is located on the Ohio River near Madison, Indiana. Fore and Aft currently operates a docking facility where only one boat at a time can stop for gas and servicing. The manager of the Fore and Aft Marina wants to investigate the possibility of enlarging the docking facility so that two boats can stop for gas and servicing simultaneously. Assume that the arrival rate is 3 boats per hour and that the service rate for each server is 9 boats per hour. (Round your answers to four decimal places.) (a) What is the probability that the boat dock will be idle? (b) What is the average number of boats that will be waiting for service? (c) What is the average time (in hours) a boat will spend waiting for service? h (d) What is the average time (in hours) a boat will spend at the dock? h (e) If customers expect to be able to be in and out of the marina within 10 minutes on average, does this system provide acceptable service? ---Select--- V since the average time a boat will…

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