SmartWafer is a wafer manufacturing company.
a. It has capacity to produce 1,000 boxes of wafer per year. They supply wafers to both advance order market and spot market. Intel wants to purchase 650 boxes of wafers at the price of $200/box. The marketing department believes that the spot market price will be $300/box. They also expect the demand of spot market to be uniformly distributed between 300 boxes and 600 boxes. What percentage of Intel’s demand can be satisfied with the advance purchase at $200/box from SmartWafer?
b. The wafer market is hot. SmartWafer decides to expand their capacity. Now it has capacity of 800 boxes/year dedicated to the spot market and the company is pretty sure that all capacity can be sold. But the wafer manufacturing process is highly unreliable. The manufacturing department estimates that the number of defective wafers will be uniformly distributed between 50 and 150 boxes. The spot market price is still $300/box. If SmartWafer accepts an order but cannot fulfill the order due to the quality issue, they have to pay $450/box as penalty.
(i) What is the basic tradeoff ?
(ii) How many customer orders can SmartWafer accept in the spot market?