An oil refinery is located on the north bank of a straight river that is 2 km wide. A pipeline is to be constructed from the refinery to storage tanks located on the south bank of the river 6 km east of the refinery. The cost of laying pipe is $400,000/km over land to a point P on the north bank and $800,000/km under the river to the tanks. Place the steps below in the correct order that they should be performed in order to determine where the point P should be located to minimize the cost of the pipeline.
1. Step 1 ___
2. Step 2 ___
3. Step 3 ___
4. Step 4 ___
- Differentiate and find the absolute minimum
- Draw a picture
- Assign a variable to the quantity that is to be minimized and name the unknowns in your picture
- Eliminate all but one of the variables in the quantity you are trying to minimize
- Find an equation relating the variables