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# hw5-1 - μ and c ﬁxed and similarly as a function of μ...

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IEOR 161 University of California, Berkeley Spring 2009 Homework 5 Due date: March 11 (in discussion session), 2010. The following are taken from “Introduction to Probability Models” by Sheldon Ross ( 9th Edi- tion ). 1. 5.36, 5.43, 5.47, 5.49. 2. This problem asks you to simulate the “optimal selling” example that was presented in class. Assume that offers arrive according to a Poisson process with rate λ = 10. The offer amounts are exponential with rate μ = 1 / (0 . 8) (or mean 0 . 8). Assume that the cost per unit time c = 1. (a) Show that the optimal threshold level for accepting an offer is y * = 1 μ ln λ . Plot y * as a function of λ (with μ
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Unformatted text preview: μ and c ﬁxed), and similarly as a function of μ and c . Does it make intuitive sense? (b) Simulate the system under the optimal threshold with the values for ( λ, μ, c ) as above 10,000 times. ( y * = 1 . 66 in this case). Plot a histogram of the seller’s proﬁt under the optimal threshold. Use the simulated samples to compute the mean, standard deviation, the 5 th-percentile, and 95 th-percentile of the optimal proﬁt. (c) Repeat part (a) for (non-optimal) threshold values of y * = 0 . 75 and y * = 3. What do you notice about the histogram? Does it make intuitive sense? 1...
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