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per-unit price c¡¡ for product

per-unit price c¡¡ for product

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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9 Your boss asks you to purchase b; units of product i for each i in a set P of products. (These products are all divisible, i.e. they can be obtained in fractional amounts.) Of course, your boss wants you to spend as little money as possible. You call up all the stores in a set S of stores, and store j gives you a per-unit price C¡¡ for product i for all i, j. (a) You decide to just order all b; units of product i from the store that gives the cheapest per-unit price for each i. Show that this is optimal. (b) Actually, there is another constraint. Your boss forgot to tell you that he does not want you to buy from too many different stores – he wants you to keep the number of stores from which you buy to at most (integer) k. Modify your formulation in (a), the resulting formulation should be an IP. (c) It turns out that the stores have special deals. If the total value of your order from store j is at least t; dollars, it will give you d; cash back. (All stores j offer such a deal, with perhaps different values of t; and d¡ .) Modify your formulation in (b), the resulting formulation should be an IP.
Transcribed Image Text:9 Your boss asks you to purchase b; units of product i for each i in a set P of products. (These products are all divisible, i.e. they can be obtained in fractional amounts.) Of course, your boss wants you to spend as little money as possible. You call up all the stores in a set S of stores, and store j gives you a per-unit price C¡¡ for product i for all i, j. (a) You decide to just order all b; units of product i from the store that gives the cheapest per-unit price for each i. Show that this is optimal. (b) Actually, there is another constraint. Your boss forgot to tell you that he does not want you to buy from too many different stores – he wants you to keep the number of stores from which you buy to at most (integer) k. Modify your formulation in (a), the resulting formulation should be an IP. (c) It turns out that the stores have special deals. If the total value of your order from store j is at least t; dollars, it will give you d; cash back. (All stores j offer such a deal, with perhaps different values of t; and d¡ .) Modify your formulation in (b), the resulting formulation should be an IP.
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