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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.

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