For each problem below, hand in an algebra formulation, and also solve using
Excel and Solver, handing in the
standard printouts.
Q1. (25 points) Problem 50 on page 161 of the course pack (Eastinghouse
capacitors)
Q2. (35 points) You are planning the staffing of maintenance technicians at a printing plant which operates on three shifts. You can use up to 8 possible technicians, each of whom can be assigned to most one shift. The costs of assigning the technicians and their certified categories of competency are as follows:
| Shift 1 | Shift 2 | Shift 3 | Certified in Category | ||||
| Technician | Cost | Cost | Cost | 1 | 2 | 3 | 4 |
| 1 | $ 280 | $ 290 | $ 300 | X | X | -- | X |
| 2 | $ 300 | $ 330 | $ 350 | -- | X | X | X |
| 3 | $ 270 | $ 280 | $ 290 | -- | -- | X | X |
| 4 | $ 180 | $ 190 | $ 200 | X | -- | -- | -- |
| 5 | $ 175 | $ 160 | $ 185 | -- | X | -- | -- |
| 6 | $ 225 | $ 225 | $ 225 | -- | X | -- | X |
| 7 | $ 295 | $ 295 | $ 315 | X | X | X | -- |
| 8 | $ 305 | $ 350 | $ 320 | -- | X | -- | X |
For example, it would cost $280 to assign technician 1 to shift 1, $290 to
assign her to shift 2, and $300 to assign her to shift 3, and she is certified
in categories 1, 2, and 4. More than one technician may be assigned to
each shift. In each category, you need at least one certified technician
assigned to each shift. Determine the least expensive way to meet your
maintenance technician staffing needs.
Q3. (40 points) Problem 34 on page 151 of the course
pack (siting drug company sales representatives). The cost of basing some
number n > 1 of sales representatives in a district is $88,000 +
$80,000n, but the cost of basing 0 sales representatives in a district is
$0. Note that this problem is fairly complicated, and you will need a
combination of some binary and several sets of general integer variables.