[Solution] Problem: Toyota is trying to determine the proper capacity - #80191
Problem: Toyota is trying to determine the proper capacity level for a new electric car. A unit of capacity gives Toyota the potential to produce one car per year. It costs $10,000 to build a unit of capacity and the cost is charged equally over the next 5 years (at $2,000 per year). It also costs $400 per year to maintain a unit of capacity (whether or not it ends up being used). Each car sells for $14,000, and incurs a variable production cost of $10,000. The annual demand for the electric car during each of the next 5 years is believed to be normally distributed with mean 500,000 and standard deviation 100,000.
The demands during different years are assumed to be independent. Profits are discounted at a 10% annual interest rate. Toyota is working with a 5-year planning
horizon. Capacity levels of 300,000, 400,000, 500,000, 600,000, and 700,000 are under
consideration. Assume that Toyota would never produce more than the demand in any particular year, i.e., that no ending inventory ever occurs. Build a simulation model that will allow Toyota to determine the best capacity level. Using the results from the simulation model, answer the following questions:
(a) What is the optimal capacity level if Toyota were risk-neutral?
(b) What is the optimal capacity level if Toyota were risk-averse? There are different ways of looking at risk; please state explicitly what measure of risk you are using.
(c) Which capacity level would you select based on your risk/return profile? Why?
(d) There is a 5% chance that the actual discounted 5-year profit for the capacity level from (a) will be less than what value?
(e) There is a 5% chance that the actual discounted 5-year profit for the capacity level from (a) will exceed what value?
(f) You can be 95% confident that the expected discounted 5-year profit from (a) is between what two values? How did you find these values?
Solution:
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