athematics True or False True or false If all the coefficien

athematics
True or False

True or false. If all the coefficients a1, a2, …, an in the objective function P = a1x1 + a2x2 + … + anxn are nonpositive, then the only solution of the problem is x1 = x2 = … = xn and P = 0.
True or false. 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 (or at least keep it unchanged).
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 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 or false. If the last row to the left of the vertical line of the final simplex tableau has a zero in a column that is not a unit column, then the linear programming problem has infinitely many solutions.
True or false. Suppose you are given a linear programming problem satisfying the conditions:
The objective function is to be minimized.
All the variables involved are nonnegative, and
Each linear constraint may be written so that the expression involving the variables is greater than or equal to a negative constant.
Then the problem can be solved using the simplex method to maximize the objective function P = -C.

True or false. The objective function of the primal problem can attain an optimal value that is different from the optimal value attained by the dual proble

Solution

Post one more question to get the remaining answers

1) The statement is TRUE, since all the coefficients (a1,a2,...,an) are negative, hence if we want the function to be maximize then all the coefficients of (x1,x2,...,xn) must be zero and the resultant P will also be zero

2) The statement is FALSE, since the pivot column identifies the variable in the simplex tableau whose value has to be decreased

3) The statement is TRUE

4) The statement is TRUE