The following model represents a simple situation of buying and selling of a seasonal product for profit:
In this formulation, the decision variables xt and yt denote, respectively, the amount of the product purchased and sold, in time period t. The given data is:
The constraints state (i) that the amount of the product on hand at the end of any period cannot exceed the storage capacity C, and (ii) that the amount of the product sold at the beginning of period t cannot exceed its availability from previous periods.
denote slack variables for the constraints (with z1 = I − y1). Show that the given model is equivalent to the formulation on page 363. b) State the dual to the problem formulation in part (a), letting ui denote the dual variable for the constraint +xi , and v j denote the dual variable for the constraint containing +y.
c) Into what class of problems does this model fall? Determine the nature of the solution for T = 3.
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