By Andrew B. Templeman (auth.)
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The simplex table is used to reduce this value off whilst still maintaining non-negative values for a11 decision and state variables. The value off can only be altered by changing the value of one or more ofthe variables in the decision set,xl, .. 2). , aN determine by how muchfwill change as Xl, .. ,XN are changed. If the value of variable Xi is increased by 0 thenfwill alter by (ai x 0). In the simplex method it is conventional and much simpler if only one decision variable is alte red in value in each table.
The visualisation of a ball rolling down a sloping plane leads to the logical conclusion that unless the ball is brought to rest against a boundary it will roll on, theoretically, forever. Thus if areal, fmite solution is to be obtained for an LP problem that solution point willlie on the boundary of the feasible region. 9 All points on constraint boundary AB are optimal variable problem in whieh the lowest eonstraint boundary runs parallel to the objeetive funetion eontours. Here any point between A and B is a solution point sinee it is feasible and gives the lowest value to f.
In order to start production of elements it is necessary to know how many elements of each type are to be produced. Furthermore it is necessary to know on which production line a particular element type is to be manufactured. The production plan, therefore, consists of a list of the numbers of each element type to be produced on each production line. If Xij is the number of elements of type i produced on line j, the list of variables is then Xl1, X12, X21> X22, X32 and X33, that is, a total of six variables.