Stanford University Department of Management Science and Engineering Optional Problem Session 1 Winter 2010 Friday, January 15, 2010 Practice Problem 1.1 (Charlie and the Chocolate) Charlie loves chocolate and spends $60 every month on buying both dark chocolate and milk chocolate from Mr. Wonka’s specialty store. After diﬀerent chocolate bundles, in order to ﬁnd his ‘optimal’ consumption basket. Given d ≥ 0 ounces of dark chocolate and m > 0 ounces of milk chocolate, Charlie describes his preference relation ± as follows: 1 (i) 0 ≤ d/m, ˆ d/ ˆ m ≤0 . 5: ( d,m ) ± ( ˆ d, ˆ m ) if and only if 2 d + m ≤ 2 ˆ d + ˆ m ; (ii) 0 . 5 ≤ d/m, ˆ d/ ˆ m ≤ 2: ( d,m ) ± ( ˆ d, ˆ m ) if and only if d + m ≤ ˆ d + ˆ m ; (iii) d/m, ˆ d/ ˆ m ≥ 2: ( d,m ) ± ( ˆ d, ˆ m ) if and only if d + 2 m ≤ ˆ d + 2 ˆ m . The price of dark chocolate is $1.25 per ounce, and the price of milk chocolate is $1 per ounce.
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This note was uploaded on 05/06/2010 for the course MSE 211 at Stanford.