Business questions
Question 1
In a job shop, effective capacity is only 50 percent of design capacity, and actual output is 80 percent of effective output. What design capacity would be needed to achieve an actual output of eight jobs per week?
Question 2
A real estate agent is considering changing her cell phone plan. There are three plans to choose from, all of which involve a monthly service charge of $20. Plan A has a cost of $.45 a minute for daytime calls and $.20 a minute for evening calls. Plan B has a charge of $.55 a minute for daytime calls and $.15 a minute for evening calls. Plan C has a flat rate of $80 with 200 minutes of calls allowed per month and a charge of $.40 per minute beyond that, day or evening.
1. Determine the total charge under each plan for this case: 120 minutes of day calls and 40 minutes of evening calls in a month.
total charge for plan A
total charge for plan B
total charge for plan C
2. Prepare a graph that shows total monthly cost for each plan versus daytime call minutes. Include the graph in your Excel file.
3. If the agent will use the service for daytime calls, over what range of call minutes will each plan be optimal?
# mins for A to be optimal
# mins for B to be optimal
# mins for C to be optimal
3. Suppose that the agent expects both daytime and evening calls. At what point (i.e., percentage of call minutes for daytime calls) would she be indifferent between plans A and B?
proportion of daytime mins
proportion of nighttime mins
Question 3
A manager must decide how many machines of a certain type to purchase. Each machine can process 100 customers per day. One machine will result in a fixed cost of $2,000 per day, while two machines will result in a fixed cost of $3,800 per day. Variable costs will be $20 per customer, and revenue will be $45 per customer.
1. Determine the break-even point for each range.
break-even point for 1 machine
break-even point for 2 machines
2. If estimated demand is 90 to 120 customers per day, how many machines should be purchased?
Question 4
An assembly line with 17 tasks is to be balanced. The longest task is 2.4 minutes, and the total time for all tasks is 18 minutes. The line will operate for 450 minutes per day.
1. What are the minimum and maximum cycle times?
minimum cycle time mins
maximum cycle time mins
2. What range of output is theoretically possible for the line?
minimum output units
maximum output units
3. What is the minimum number of workstations needed if the maximum output rate is to be sought?
minimum # workstations
4. What cycle time will provide an output rate of 125 units per day?
cycle time mins
5. What output potential will result if the cycle time is (1) 9 minutes? (2) 15 minutes?
output potential for cycle of 9 minutes units
output potential for cycle of 15 minutes units
Question 5
A manager wants to assign tasks to workstations as efficiently as possible and achieve an hourly output of 33⅓ units. Assume the shop works a 60-minute hour. Assign the tasks shown in the accompanying precedence diagram (times are in minutes) to workstations using the following rules:
1. In order of most following tasks. Tiebreaker: greatest positional weight.
Station Tasks assigned Total time at station Idle time at station
1
2
3
4
2. In order of greatest positional weight. Tiebreaker: most following tasks.
Station Tasks assigned Total time at station Idle time at station
1
2
3
4
3. What is the efficiency?
efficiency is % (two decimal places)
Question 6
Arrange six departments into a 2 × 3 grid so that these conditions are satisfied: 1 close to 2, 5 close to 2 and 6, 2 close to 5, and 3 not close to 1 or 2.
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