Assume that we are solving an LP (maximization problem) with the simplex method.
ID: 3210061 • Letter: A
Question
Assume that we are solving an LP (maximization problem) with the simplex method. At the current basic feasible solution, z 75 and xi has a reduced cost of -5.0 (where reduced costs are calculated as Taj-c). It is determined that X1 is the next entering variable, and that xi will replace the basic variable x3 (i.e., xj is the leaving variable) based on a minimum ratio of 2. 1. (a) What numerical value will have after the pivot (i.e., after x1 enters the basis and x3 leaves the basis)? (b) What numerical value w the objective function have after the pivot (i.e., after xi enters the basis and X3 leaves the basis)?Explanation / Answer
(a) x1 will replace x3 in the basis. So new value of x1 will be equal to the value x3 had before.
(b) Numerical value of objective function = previous value + (j x minimum ratio )
= previous value + ((c,j - T aj ) x minimum ratio)
= 75 + (-(-5) x 2) = 85