Problem:
It is spring 2000, and TMMC has indeed just been chosen to produce the new Lexus RX 330 line, with the first units deliverable in 2003. Toyota must now determine the amount of annual production capacity it should build at TMMC.
Toyota's goal is to maximize the profit from the RX 330 line over the five years from 2003-2007. These vehicles will sell for an average of $37,000 and incur a mean unit production cost of $28,000 (here, $ = the Canadian dollar).
10,000 units of annual production capacity can be built for $50M (M=million) with additional blocks of 5,000 units of annual capacity each costing $15M. Each block of 5,000 units of capacity will also cost $5M per year to maintain, even if the capacity is unused.
Assume that the number of units actually sold each year will be the lesser of the demand and the production capacity.
Marketing has provided three vehicle estimated demand scenarios with associated probabilities as follows:
Demand 2003 2004 2005 2006 2007 Probability
Low 10,000 10,500 11,000 11,500 12,000 0.25
Moderate 15,000 16,000 17,000 18,000 19,000 0.50
High 20,000 24,000 26,000 28,000 30,000 0.25
Required:
Question 1) To maximize profit earned during this period, which production capacity should TMMC in 2000 decide to build - 10,000, 15,000, 20,000, 25,000, or 30,000 cars? Justify your choice. Solve the given numerical problem and illustrate step by step calculation.