For each problem listed below:
Q1. (30 points) Problem 19(b) on pages 103-104 of the
course pack (setting up a rock concert). From your spreadsheet solution,
identify the critical path, or all critical paths if there is more than one.
(Note: ignore the network diagram immediately above the problem; it is in a
different style than the one I drew in class, and is for a different problem.)
Q2. (30 points) In the same setting as Q1, assume that you have the option of shortening activities as shown in the table below. You have a budget of $855 to shorten the preparation time for the concert as much as possible. How quickly can you complete the project? (Note: while this problem resembles the "crashing" problem we did in class, the objective function and constraints are not quite the same -- in class, we had to find the cheapest way to finish by a given deadline. Here, we must find the fastest way to finish within a given budget.)
| Code |
Activity |
Cost/Day to Shorten | Max Days can be Shortened |
| A | Find site | $ 100.00 | 1.0 |
| B | Find engineers | $ 60.00 | 1.5 |
| C | Hire opening act | $ 50.00 | 3.0 |
| D | Set up broadcast ads | $ 80.00 | 0.5 |
| E | Set up ticket agents | $ 200.00 | 2.0 |
| F | Prepare electronics | $ 250.00 | 1.5 |
| G | Print ads | $ 70.00 | 3.0 |
| H | Set up transport | $ 50.00 | 0.5 |
| I | Rehearsals | $ 300.00 | 0.5 |
| J | Details | $ 400.00 | 1.0 |
Q3. (40 points) Problem 55 on page 163 of the course pack
(Monsanto). Assume that you should produce at least 359 million
pounds of the product -- that is, production of more than 359 million
pounds is permissible. You are also allowed to leave any reactor off for
the entire year, in which case its cost is $0 and it produces 0 pounds of the
product.