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Unformatted text preview: IEOR 162 Linear Programming Spring 2007 Homework 4 Solutions 3.12.4 (4 points) Data: T = the number of months p t = purchase price per 1000 bushels of wheat during month t s t = selling price per 1000 bushels of wheat during month t Variables: x t = amount of wheat (in 1000 bushel units) to purchase during month t y t = amount of wheat (in 1000 bushel units) to sell during month t I t = inventory of wheat (in 1000 bushel units) at the end of month t Formulation: max T ∑ t =1 ( s t y t- p t x t ) s.t. I = 6 (1) I t = I t- 1 + x t- y t t = 1 , . . . , T (2) y t ≤ I t- 1 t = 1 , . . . , T (3) I t ≤ 20 t = 1 , . . . , T (4) x t , y t , I t ≥ t = 1 , . . . , T (5) The objective maximizes the revenue earned from selling minus the costs of purchasing wheat. Constraint 1 sets our initial inventory to 6000 bushels as specified. Constraint set 2 indicates that the inventory on hand at the end of month t is equal to last month’s inventory plus whatever we buy minus whatever we sell. Constraint set 3 asserts that we cannot sell more than the amount we had on hand at the end of thesell....
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This homework help was uploaded on 04/02/2008 for the course IEOR 162 taught by Professor Zhang during the Spring '07 term at Berkeley.
- Spring '07