# Cost Optimization - Calculus Weiland

- Author:
- Mr Weiland

- Topic:
- Calculus

Congratulations on now being an Engineer! Your company wants to build a bridge over a lake for the most efficient way to transport lumber. The Lumber Processing Plant is 14 miles east and 12 miles north of the Lumber Field. (Assume the Lumber Field is located at (0,0)). The lake is bounded by the curves y = -.04(x-7)^2+9.5 and y = .03(x-8)^2+3. Your boss gives you the following restrictions: 1) The bridge must run precisely south to north and 2)The roads to and from the bridge will be straight lines.
It will cost $10 thousand per mile to build a road from the Lumber Field to the Bridge, $15 thousand per mile for the bridge, and $12 thousand per mile from the bridge to the Processing Plant.
a.)Your job is to decide exactly where to build the bridge to minimize the cost of the project.(Use your Graphing Calculator to find extrema. Do NOT take the derivative)
b.) Find the maximum and minimum cost of the project (between x=0 and x=14) and calculate how much money you would save your company.
c.) Using Geogebra tools, create a cost function to prove your answers for part a) and b) are correct. (You will need to add points, segments, and functions)
Show all work and be sure to explain each solution thoroughly.