The Baez Computer Company produces two models of computers, A and B. It wants to plan how many computers to produce next month to maximize profits. Producing these computers requires wiring, assembly and inspection time. Each computer produces a certain level of profits but faces only a limited demand. There are also a limited number of wiring, assembly and inspection hours available in each month. The data for this problem is summarized in the following table.
| Computer | Profit per | Maximum demand for | Wiring Hours | Assembly Hours | Inspection Hours |
| Model | Model ($) | product | Required | Required | Required |
| A | 30 | 80 | .4 | .5 | .2 |
| B | 40 | 90 | .5 | .4 | .3 |
| Hours Available | 50 | 50 | 22 |
Answer the multiple choice below using this spreadsheet model (below). You do not need to fill in any information on the sheet. Highlight your choice for each below.
| A | B | C | D | E | |
| 1 | Baez Computer Company | ||||
| 2 | |||||
| 3 | A | B | |||
| 4 | Number to make: | Total Profit: | |||
| 5 | Unit profit: | ||||
| 6 | |||||
| 7 | Constraints: | Used | Available | ||
| 8 | Wiring | ||||
| 9 | Assembly | ||||
| 10 | Inspection | ||||
| 11 | ‘A’ Demand | ||||
| 12 | ‘B’ Demand | ||||
- What formula should be entered in cell E5 to compute total profit?
a. =B4*C4+B5*C5
b. =SUMPRODUCT(B4:C4,B5:C5)
c. =SUM(B5:C5)
d. =SUM(E8:E10)
(continued from above)
- What formula should be entered in cell D8 to compute the amount of wiring used?
a. =B4*B5+C4*C5
b. =SUMPRODUCT(B8:C8,$B$4:$C$4)
c. =SUM(B5:C5)
d. =SUM(E8:E10)
- Which cells should be ‘changing’ cells (decision cells) in this problem?
- B4:C4
- E5
- D8:D10
- E8:E10
- Which cells should be the ‘left-hand-side’ constraint cells in this problem?
- B4:C4
- E5
- D8:D12
- E8:E12
- Which of the following statements will represent the constraint for just assembly hours?
a. B4:C4 ≤ B5:C5
b. D9 ≤ E9
c. D8:D10 ≤ E8:E10
d. E8:E10 ≤ D8:D10
P1. M.Scott Paper Mill is a small-scale paper company which has four machines to produce four different types of papers. Each type of paper must go through processing on each of four machines. The manufacturing time (in minutes) per unit of paper produced is in the following table:
| Time required (in minutes) | ||||
| Paper Type | ||||
| Machine Type | A | B | C | D |
| 1 | 2.4 | 1.2 | 3.2 | 2.7 |
| 2 | 2.1 | 2.4 | 3.3 | 3.2 |
| 3 | 1.6 | 0.9 | 5.1 | 2.6 |
| 4 | 2.5 | 2.5 | 6.5 | 3.2 |
(continued from above)
The maximum time allotted for each machine is 32 hours per week and at least 100 units of each type of paper should be made using these machines during the week.
Profit per unit is:
| PaperType | A | B | C | D |
| Profit ($) | 0.25 | 0.32 | 0.5 | 0.44 |
What are all of the constraints for this model? List the constraints here. Are all of the constraints needed for this model? Which machine constraint has the most important impact on paper production? Explain briefly.
What is the optimal solution in terms of the objective function and decision variables?
Is there only one optimal solution for this problem? Yes/No and briefly explain. (You do not need to use Solver to answer this question.)
Answer the following multiple-choice items by highlighting your choice.
1. Which activities have slack in the following diagram?
- A, C, D, F
- B, E
- A, C, D, E
- B, D, E
2. What is the latest finish time for activity D in the following diagram?
- 6
- 13
- 14
- 15
3. What is the earliest start time for activity D in the following diagram?
- 3
- 4
- 6
- 7
4. What are the immediate predecessors of activity D in this network?
- A, B, C
- B, C
- E, F
- E, G, H
P1. Waveland Enterprises needs to manage a project, which consists of the following set of activities:
| Task | Duration | I.P.s |
| A | 1 | – |
| B | 4 | A |
| C | 3 | B |
| D | 3 | C |
| E | 2 | B |
| F | 4 | E |
| G | 2 | D, F |
Construct a network diagram for this project. What are all possible paths for this project? List the paths as: A-B-C… What is the critical path(s)? How long will it take to complete this project?
P2. Assume that the following project has the same IPs as in the problem above.
| Activity | Normal | Crash | Normal | Crash | Slope |
| A | 5 | 3 | $6,000.00 | $8,000.00 | $1,000.00 |
| B | 3 | 2 | $18,000.00 | $19,000.00 | $1,000.00 |
| C | 4 | 2 | $14,000.00 | $19,000.00 | $2,500.00 |
| D | 7 | 4 | $6,000.00 | $9,000.00 | $1,000.00 |
| E | 6 | 1 | $9,000.00 | $14,000.00 | $1,000.00 |
| F | 5 | 3 | $12,000.00 | $14,000.00 | $1,000.00 |
| G | 4 | 2 | $3,500.00 | $7,500.00 | $2,000.00 |
What would be the critical time?
If it is possible to crash the project to 1 less than the critical time (e.g., 19 CT crashed to 18), what are all the possible ways to do that with the minimum increase in cost? Be sure to support your answer with a brief explanation.
