1. A manucaturing shop is designed to operate most effeciently at an output of 550 units per day. In the past month the plant produced 490 units. What was the capacity utilization rate last month?
2. A company has a factory that is designed so that it is most efficient ( average unit cost is minimized) when producing 15,000 units of output each month. However, it has an absolute maximum output capability of 17,250 units per month, and can produce as little as 7,000 units per month without corporate headquarters shifting production to another plant. If the factory produces 10,925 units in October, what is the capacity utilization rate in October for this factory?
3. Hoosier Manufacturing operates a production shop that is designed to have the lowest unit production cost at an output rate of 100 units per hour. In the month of July, the company operated the production line for a total of 175 hours and produced 16,900 units of output. What was its capacity utilization rate for the month?
4. AlwaysRain Irrigation, Inc., would like to determine capacity requirements for the next four years. Currently two production lines are in place for making bronze and plastic sprinklers. Three types of sprinklers are available in both bronze and plastic: 90-degree nozzle sprinklers, 180-degree nozzle sprinklers, and 360-degree nozzle sprinklers. Management has forecast demand for the next four years as follows:
Yearly Demand
Plastic 90
1 (000s) - 32
2 (000s) - 44
3 (000s) - 55
4 (000s) - 56
Plastic 180
1 (000s) - 15
2 (000s) - 16
3 (000s) - 17
4 (000s) - 18
Plastic 360
1 (000s) - 50
2 (000s) - 55
3 (000s) - 64
4 (000s) - 67
Bronze 90
1 (000s) - 7
2 (000s) - 8
3 (000s) - 9
4 (000s) - 10
Bronze 180
1 (000s) - 3
2 (000s) - 4
3 (000s) - 5
4 (000s) - 6
Bronze 360
1 (000s) - 11
2 (000s) - 12
3 (000s) - 15
4 (000s) - 18
Both production lines can produce all the different types of nozzles. The bronze machines needed for the bronze sprinklers required two operators and can produce up to 12,000 sprinklers. The plastic injection molding machine needed for the plastic sprinklers requires four operators and can produce up to 200,000 sprinklers. Three bronze machines and only one injection molding machine are available. What are the capacity requirements for the next four years? (Assume that there is no learning.)