The owner of a millwork shop is considering three 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. (10 points) Location (Unit: $1000) Costs A B C D Fixed $700 $1,000 $1,100 $1,200 Variable $28 $18 $20 $30
Step 1. Formulate Total Cost (TC) functions for each option.
Step 2. Draw a graph with Total Cost Functions. (Optional, NOT required. You may use your graphic calculator or online graphic web services such as fooplot.com, desmos.com, etc. for plotting these total cost functions in a graph.)
Step 3. Compute all meaningful cross-over point(s) (i.e. switch point(s)) to make location decisions. Your goal is to minimize the total costs according to the volume in this analysis.
Step 4. Analyze the cases and determine the best option for specific quantity ranges. (Please draw a conclusion by specifying which option is preferred in a quantity range, and which option(s) is never preferred.)