Ma170 Wk3 Assignment

True or False

Carlos Lopez

Grantham University

True or False

1)  True or false. If all the coefficients a1, a2, …, an in the objective function P = a1x1 +a2x2 + … + anxn are non-positive, then the only solution of the problem is x1 = x2 =… = xn and P = 0.

TRUE: all the coefficients are non-positive so if one of the xi becomes positive (so not equal to 0) the value of the objective function would subsequently decrease : In other words, the only possibility to stay at the optimum is x1 = x2 = … = xn = 0 then P = 0

2)  The pivot column of a simplex tableau identifies the variable whose value is to be decreased in order to increase the value of the objective function and finally it changed but given that (or at least keep it unchanged).

True. The simplex method is an iterative process. Starting at a good starting solution (a corner point – usually the origin), each iteration moves to another corner point with a better (or at least not worse) value of the objective function. Iteration stops when the best solution (if it exists) is found.

3) True or false. The ratio associated with the pivot row tells us by how much the variable associated with the pivot column can be increased while the corresponding point still lies in the feasible set.

TRUE: The smallest ratios chosen during each pivoting steps guarantee that the solution stays in the region. In order to stay in the feasible set the variable associated with the pivot column can be increased until the corresponding ratio is reached.

4) True or false. At any iteration of the simplex procedure, if it is not possible to compute the ratios or the ratios are negative, then one can conclude that the linear programming problem has no solution.

TRUE: The linear programming problem will have no solution if the simplex method breaks down during any step, and as such as when all the ratios are negative or if the computation is impossible or incorrect.

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