Given: You are in charge of a large construction project involving three separate sites some miles apart. Site 1 requires 1000 cu.yds. of concrete; site 2 requires 3000 cu.yds.; and site 3 requires 2000 cu.yds. I own three concrete batch plants which I prefer to draw from: plant 1 can supply 2000 cu.yds., plant 2 can provide 1000 cu.yds., and plant 3 can provide 2000 cu.yds. If my three batch plants cannot supply sufficient concrete, I can acquire concrete from an outside source at a cost of $20/cu.yds. if hauled to site 1, $22/cu.yds. if hauled to site 2, and $24/cu.yds. if hauled to site 3. Normal concrete costs from my plants (delivered) are as follows:
|
Site 1 |
Site 2 |
Site 3 |
|
|
Batch Plant 1 |
10 |
15 |
20 |
|
Batch Plant 2 |
12 |
10 |
16 |
|
Batch Plant 3 |
15 |
7 |
22 |
Required: Solve this problem so that concrete costs are minimized.