On a manufacturing capacity problem in high-tech industry

We modify the market-clearing price proposed by Pangburn and Sundaresan for an optimal production model in high-tech industry. Under our assumptions the market-clearing price depends also on the demand rate; this hypothesis makes the problem more difficult but returns an optimal production rate which is decreasing in a left neighborhood of the final time, as one would expect for economic reasons. As the solution to the fundamental optimal control problem is characterized through some equations which do not have explicit solutions, we have to solve the capacity problem only numerically. To this purpose we present a numerical procedure to perform a satisfactory, though approximate, analysis of the model. Mathematics Subject Classification: 91B38, 90B30, 49N90, 90-04