Consider the following LP:Maximize2 1 4 2 3 3 3 4z = x + x + x + xSubject to x1 + x2 + x3 = 4 x1 + 4x2 − 4x4 = 8 x1, x2, x3  0, x4  0(a) Convert the LP given above to the standard form in which the necessary slack, excess and artificial variables are added.(b) Convert the LP given above to the canonical form (Hint: Do not use any slack, excess, and artificial variables).(c) Using the relevant formulas, determine the tableau to the LP model where 1x and 2x are the basic variables. Is the solution optimal? If not, start with this solution and find the optimal solution.(d) Write the dual of the problem

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3. Consider the following LP: Мaximize z = 2x, +4 x, +3x, +3 x4 Subject to X +x, +x3 = 4 X, +4x, – 4x4 = 8 X1, X2, X3 2 0, x4 <0 (a) Convert the LP given above to the standard form in which the necessary slack, excess and artificial variables are added. (b) Convert the LP given above to the canonical form (Hint: Do not use any slack, excess, and artificial variables). (c) Using the relevant formulas, determine the tableau to the LP model where x, are the basic variables. and find the optimal solution. (d) Write the dual of the problem. X1 and the solution optimal? If not, start with this solution 3. Consider the following LP: Мaximize z = 2x, +4 x, +3x, +3 x4 Subject to X +x, +x3 = 4 X, +4x, – 4x4 = 8 X1, X2, X3 2 0, x4 <0 (a) Convert the LP given above to the standard form in which the necessary slack, excess and artificial variables are added. (b) Convert the LP given above to the canonical form (Hint: Do not use any slack, excess, and artificial variables). (c) Using the relevant formulas, determine the tableau to the LP model where x, are the basic variables. and find the optimal solution. (d) Write the dual of the problem. X1 and the solution optimal? If not, start with this solution