1. A manufacturing firm is considering three alternatives for automation. They anticipate annual production volume to be 75,000 units. The costs for each alternative are as shown:
| |Alternative | | |1 |2 |3 | |Annual Fixed Costs |60,000 |$180,000 |$300,000 | |Variable Cost/Unit |$0.65 |$0.55 |$0.40 | | | | | |
|a. |What sales price must be charged for Alternative 1 to break even? | |b. |What sales price must be charged for Alternative 2 to break even? | |c. |What sales price must be charged for Alternative 3 to break even? | | | |
|a. |$60,000 + ($.65)(75,000) = 75000S => S = $1.45 | | | | |b. |$180,000 + ($.55)(75,000) = 75000S => S = $2.95 | | | | |c. |$300, 000 + ($.40)(75,000) = 75000S => S = $4.40 | | | |
2. An ATM machine provides four sequential steps in processing a transaction. Over the last quarter, the reliability of each of these steps was 0.92, 0.97, 0.95 and 0.90. What is the overall reliability of the machine? How much can reliability be improved if the reliability of the fourth step is increased to 0.98?
RS = (0.92)(0.97)(0.95)(0.90) = 0.7630
If the reliability of the fourth step is increased to 0.98, RS = (0.92)(0.97)(0.95)(0.98) = 0.8308
3. An order fulfillment process normally operates two shifts a day, six days per week. Under normal conditions, 380 orders can be processed per shift. What is the weekly capacity?
Capacity = (380/shift)(2 shifts/day)(6 days/week) = 4560 orders/week
4. A small electronics company assembles power supplies for use in computers, printers and Fax machines. They want to set up an assembly line to make their operation more efficient and plan to use line balancing with the longest-task-time heuristic. The demand for power supplies is 70 per hour, and the productive time per hour is 52 minutes. The following table provides details on their operation.
|Task |Time (in minutes) |Predecessors |
|A |.54 |none |
|B |.34 |A |
|C |.11 |A |
|D |.09 |A |
|E |.43 |B, C |
|F |.22 |D |
|G |.62 |E |
|H |.35 |F, G |
|I |.21 |H |
|J |.57 |H |
|K |.33 |I, J |
| | | |
|a. |What is the cycle time? | |b. |What is the theoretical minimum number of workstations? | |c. |What tasks go into the first workstation? | |d. |How many workstations are needed for the entire line? | |e. |What is the assembly-line efficiency? | | | |