Problem: The We Haul Trucking Company hauls gravel from two quarries to five construction sites. Quarries A and B charges $17 and $21 per ton, respectively, for gravel; they each have 400 tons of gravel available per week. We Haul has contracted to deliver 110, 227, 82, 148, and 193 tons of gravel per week to construction sites, 1, 2, 3, 4, and 5, respectively. We Haul figures that it costs them $0.10 per ton per mile of gravel hauled due to wear and tear on their trucks. The table below lists the distances (in miles) between the quarries and the construction sites.
|
Construction site (miles)
|
|
1
|
2
|
3
|
4
|
5
|
|
Quarry A
|
77
|
23
|
17
|
42
|
31
|
|
Quarry B
|
58
|
16
|
33
|
27
|
15
|
- Formulate a mathematical linear programming model to determine the cost minimizing way to fulfill the gravel contracts. Type the model in worksheet 1 of your excel file.