Consider TXL, an original equipment manufacturer that produces mobile communication devices with very short product life cycles, for telecom companies all around the world who brand and sell these devices under their name. Due to market forces, TXL has to innovate and introduce a new version of their products every year. Demand characteristics of its products make forecasting and purchase decisions very challenging for the components that go into manufacturing.

Sourcing of the LCD module has historically been problematic, with significant observations of insufficient quantities in the recent years, and the management at TXL would like to develop a solid approach to their decision process and contractual relationship with its supplier, Pavan, Inc.

For the upcoming year, Pavan has announced a unit wholesale price of $44.5 for these modules, which are custom designed (in terms of size, resolution, technology, and interface) for the current generation of TXLs devices and has little value if not used. It is estimated that TXL could liquidate the leftover modules in a secondary market at a 60% loss. To build the current generation of devices, TXLs cost for all other components and material was $131 per unit, and the average sale price was expected to be $200 per unit. TXLs demand forecast is Normal distributed with mean 9400 and standard deviation 6100. Assume Pavans unit cost for each module to be $20.

How many LCD modules should be shipped to TXL in order to maximize the total supply chain profits? Calculate the resulting expected profits for both TXL and Pavan.