Consider the following LPP: maximize: c1x1 + c2x2subject to: a1x1 +a2x2 = b here a1 > a2 > 0, and c1 > c2 > 0, and b > 0. (a) Change this problem to canonical form. (b) Assume a1/a2 − c1/c2 = 0 and use the two-phase method to solve this LPP.
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Consider the following LPP:
maximize: c1x1 + c2x2
subject to: a1x1 +a2x2 = b
here a1 > a2 > 0, and c1 > c2 > 0, and b > 0.
(a) Change this problem to canonical form.
(b) Assume a1/a2 − c1/c2 = 0 and use the two-phase method to solve this LPP.
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- 23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes 1/2 of the food and 1/3 of the manufactured goods. Manufacturing consumes 1/2 of the food and 2/3 of the manufactured goods. Assuming the economy is closed and in equilibrium, find the relative outputs of the farming and manufacturing industries.Solve the following LP model using the simplex method. Minimize z = −4x1 + 6x2 − 2x3 + 4x4 Subject to: x1 + 2x2 + 2x3 + 4x4 ≤ 402x1 − x2 + x3 + 2x4 ≤ 84x1 − 2x2 + x3 − x4 ≤ 10x1, x2, x3, x4 ≥ 0Consider the following problem. Minimize Z=3X1+2X2+4X3 Subject to 2X1+X2+3X3=60 3X1+3X2+5X3≥120 and X1, X2, X3≥0 Using the two-phase method, work through the simplex method to solve the problem
- Suppose that we want to optimize the function V = x2 + y2 + z3, subject to the restriction xyz = 4, using the Lagrange multipliers technique. If λ corresponds to the multiplier used when defining the Lagrange function, then one of the equations of the system to be solved corresponds to:Solve the following systems by using Gaussian Elimination with out partial pivoting x1 − 3x2 + 2x3 + x4 = −4 2x1 − 6x2 + x3 + 4x4 = 1 −x1 + 2x2 + 3x3 + 4x4 = 12 − x2 + x3 + x4 = 0.Suppose we want to maximize the function V = x2y, with x, y positive, subject to the constraint x2 + 2y2 = 6, through the Lagrange multipliers technique. When solving the system corresponding to this problem, the following relationship between the variables is obtained: