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 21 on page 34 of the course pack (finished and unfinished tables and chairs; just follow the instructions above -- do not bother with parts (b) and (c)).
Q2. (35 points) Problem 22 on page 34 of the course pack (ChemCo).
Q3. (35 points) Delta products company is facing the following production cost, holding cost, and order pattern for the next six months:
| Unit | Unit | ||
| Production | Holding | ||
| Month | Cost | Cost | Orders |
| 1 | $ 108.00 | $ 2.50 | 100 |
| 2 | $ 92.50 | $ 2.35 | 125 |
| 3 | $ 98.00 | $ 2.20 | 150 |
| 4 | $ 105.00 | $ 2.10 | 145 |
| 5 | $ 112.00 | $ 2.50 | 110 |
| 6 | $ 103.50 | $ 2.75 | 115 |
For example, you must deliver 100 units in month 1, it costs you $108 to produce a unit in month 1, and $2.50 to hold a unit in inventory from month 1 to month 2 (you assess inventory costs on month-end inventories). The factory can produce at most 130 units per month, and you have an agreement with your production workers' union that each month's production must cannot fall by more than 25 units from the prior month's production. You can hold up to 50 units in inventory, and you want to have at least 10 units left in inventory at the end of month 6. You are starting with 30 units in inventory, and last month's production level was 100 units. You want to find the cheapest possible way to obey all the above constraints and meet all the orders shown in the table.