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QBA200A Case Preparation #7 Due 10:00 AM, Monday, November 28th Submit Answers to ForClass "Case Preparation #7" https://app.forclass.com/x/read?
Microsoft Word - Case preparation 7
Pricing with Uncertain Demand
Consider a market in which you make and sell a product, by charging a single (fixed) price, P. The demand follows the pattern:
Demand = 500*exp(-a*P)
However, the value of a is unknown at the time you need to determine the price P. Let’s assume that a, which represents the consumers’ sensitivity to the price, is uniformly distributed in the range [0.01,0.05].
After you set the price, demand is realized, and then you must produce and sell, to match demand.
Your cost per unit is $20.
Questions:
(a) Suppose that a was equal to its average value, a=(0.01+0.05)/2=0.03. What would be the optimal price, and optimal profit? [Hint: this is a nonlinear optimization problem]
(b) Build a simulation model that allows for a randomized a according to the uniform distribution. Replicate the simulation 1,000 times using Data Table. Calculate the (i) mean profit, (ii) standard deviation, and (iii) 95% confidence interval of the true mean.
