Set up the simplex matrix used to solve the linear programming problem. Assume all variables are nonnegative. Maximize  f = 6x + 9y + 6z  subject to 4x  +  7y  +  9z  ≤  100   6x  +  5y  +  z  ≤  135   x  +  4y  +  9z  ≤  30

Consider the problemMaximize z = x1 + 5x2 + 3x3subject tox1 + 2x2 + x3 = 62x1 - x2 = 8x1, x2, x3 >= 0The variable x3 plays the role of a slack. Thus, no artificial variable is needed in the firstconstraint. In the second constraint, an artificial variable, R, is needed. Solve the problemusing x3 and R as the starting variables.

Find X₁ and X₂ that maximize the objective function Z = 3x₁ + 5×₂2 with the constraint function 2x, 8 3X₁ ≤ 15 6X₁ + 5X₂ > 30 = Using the simplex method.

Need only a handwritten solution only (not a typed one).

A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chessboard. On the second square, the King would place two grains of​ wheat, on the third​ square, four grains of​ wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining​ squares, how many grains of wheat should be placed on a square 16​? Also, find the total number of grains of wheat on the board at this time and their total weight in pounds.​ (Assume that each grain of wheat weighs​ 1/7000 pounds.)