2. [Location Strategy - Locational Cost-Volume Analysis with Switching Points (15 pts)] The owner of a millwork shop is considering six alternative locations for a new plant for building embossed-and-clad steel exterior doors for residences. Fixed and variable costs follow. Since the plant ships nationwide, revenue is assumed the same regardless of plant location. Identify the range over which each location is best.

Costs (Unit: 1M) Location A B C D E F

Fixed Cost $6 $10 $13 $15 $18 $23

Variable Cost $4 $5 $2 $5 $4 $1

(a) Step 1.Formulate Total Cost (TC) functions for each option.

Step 2. Plot all the total cost functions in a graph. (Optional, NOT required. BUT, Highly Recommended) You can plot it by hand on a scratch paper or use any online graphical software/graphical calculator. (For example, please refer to http://fooplot.com or https://www.desmos.com/calculator)

(b) Step 3. Compute all meaningful cross-over points (switching points) to make location decisions according to volume. (Hint: Please disregard all redundant cross-over points for the minimization of the total costs.)

(c) Step 4. Analyze the cases and determine the best option for specific quantity ranges. (Please state which options are preferred in specific quantity ranges, and which options are never preferred.)