bv_cvxbook_extra_exercises

# At the end of the investment period if the stock is

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Unformatted text preview: t not sold; when dj &gt; qj , dj − qj is the amount of unmet demand.) The revenue from selling the products is pT s, where p ∈ Rn is the vector of product prices. The proﬁt is pT s − cT r. (Both d and q are real + vectors; their entries need not be integers.) You are given A, c, and p. The product demand, however, is not known. Instead, a set of K possible demand vectors, d(1) , . . . , d(K ) , with associated probabilities π1 , . . . , πK , is given. (These satisfy 1T π = 1, π 0.) You will explore two diﬀerent optimization problems that arise in choosing r and q (the variables). I. Choose r and q ahead of time. You must choose r and q , knowing only the data listed above. (In other words, you must order the raw materials, and commit to producing the chosen quantities of products, before you know the product demand.) The objective is to maximize the expected proﬁt. II. Choose r ahead of time, and q after d is known. You must choose r, knowing only the data listed above. Some time after you have ch...
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## This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.

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