9 Your boss asks you to purchase b; units of product i for each i in a set P ofproducts. (These products are all divisible, i.e. they can be obtained infractional amounts.) Of course, your boss wants you to spend as little moneyas possible. You call up all the stores in a set S of stores, and store j gives youa 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 givesthe 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 hedoes not want you to buy from too many different stores – he wants youto keep the number of stores from which you buy to at most (integer) k.Modify your formulation in (a), the resulting formulation should be anIP.(c) It turns out that the stores have special deals. If the total value of yourorder from store j is at least t; dollars, it will give you d; cash back. (Allstores j offer such a deal, with perhaps different values of t;and d¡ .)Modify your formulation in (b), the resulting formulation should be anIP.

The boss asks you to purchase bi units of product i for each i in a set P of products. You decide to…

Answered: per-unit price c¡¡ for product

Business

Economics

per-unit price c¡¡ for product

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter6: Demand Relationships Among Goods

Section: Chapter Questions

Problem 6.5P

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Question

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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