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Zen Lighting distributes a lamp design in two customer segments (i = 1 and 2). The annual demand is linearly defined by the function Di=Ai-BiPi and is defined by A1=4100 B1= 15 and A2=8300 B2= 48. The lamp production cost is $24/unit. The maximum annual supply is 5000 units.
1. Derive the optimal price and demand for each segment?
2. What is the Net Supply Chain Profit?
3. Zen Lighting abandons the linear demand model for the higher demand (i=1) segment. Instead it assumes that at a price of $140 the demand is normally distributed with mean of 3300 units and a Std. Dev of 1200 units. If the i=2 price is set at your answer from (i) what quantity should be allocated to the higher price segment?
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