For each problem below, hand in an algebra formulation, and also solve using
Excel and Solver, handing in the standard printouts.
Q1. (30 points) Problem 50 on page 161 of the course
pack (Eastinghouse
capacitors).
Q2. (35 points) Your machine shop has five jobs to do today. Each job must be done by exactly one machine, but a machine can do more than one job. For each machine, there is a setup cost for the regular work day. Once this cost is paid, you can use the machine for up to 8 hours; if you do not pay the setup cost, you cannot use the machine today. If you set up a machine for the regular work day, you may also elect to set up the machine for overtime, in which case there is an additional cost and you may use the machine for up to 2 more hours. On the other hand, if you do not set up a machine for the regular work day, it cannot be used for overtime. The costs are as follows:
Setup Cost | Overtime Setup Cost | |
Machine 1 | $ 600 | $ 190 |
Machine 2 | $ 700 | $ 200 |
Machine 3 | $ 550 | $ 275 |
Machine 4 | $ 675 | $ 150 |
Machine 5 | $ 585 | $ 195 |
Thus, if you pay $600, you can use machine 1 for up to 8 hours, and if you pay $600 + $190 = $790, you may use machine 1 for up to 8 + 2 = 10 hours. The number of hours each job takes on each machine is as follows:
Job 1 | Job 2 | Job 3 | Job 4 | Job 5 | |
Machine 1 | 3.0 | 4.0 | 5.5 | 2.5 | 3.1 |
Machine 2 | 3.8 | 4.9 | 6.4 | 2.9 | 2.7 |
Machine 3 | 3.6 | 4.8 | 5.5 | 3.8 | 2.8 |
Machine 4 | 2.9 | 5.3 | 5.6 | 2.9 | 1.9 |
Machine 5 | 3.1 | 6.0 | 5.1 | 2.6 | 2.5 |
Figure out the cheapest way to get all 5 jobs done today.
Q3. (35 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.