Find the optimal solution for the following problem. (Round your answers to 3 decimal places.)14x + 13y + 5zMaximize C =subject toand9x + 11y + 18z ≤ 6114x + 15y + 12z ≤ 122x ≥ 0, y ≥ 0, z ≥ 0.a. What is the optimal value of x?Xb. What is the optimal value of y?y

Introduction: The simplex method is a method for testing vertices as potential solutions in a…

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College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter5: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 2P

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Find the optimal solution for the following problem. Minimize C = 4x + 12y + 3z subject to 15x + 5y + 12z ≥ 75 6x + 2y + 8z ≥ 150 and x ≥ 0, y ≥ 0. What is the optimal value of x? What is the optimal value of y? What is the optimal value of z? (Round your answer to 3 decimal places.)
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A firm produces a good from two raw materials X and Y which can be bought at unit prices of pX and pY , respectively. Given a quantity x of X and a quantity y of Y , the firm can produce a quantity of goods q given by the production function q(x, y) = 3x^1/3y^2/3. The firm has a budget of $1,000 with which to buy the raw materials X and Y at unit prices of $2 and $3, respectively. Find the optimal quantities x and y that maximizes production subject to the budget constraint.
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Q1:- How do you determine if an LP problem has alternative optimal solutions. Min z = 4x1 + 2x2 s.t. 3x1 + x2 ≥ 27 -x1 - x2 ≤ 21 x1 + 2x2 ≥ 30 x1 and x2 are unrestricted .

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Find the optimal solution for the following problem. (Round your answers to 3 decimal places.) Maximize C = 14x + 13y + 5z subject to 9x + 11y+ 18z ≤ 61 14x + 15y + 12z ≤ 122 x ≥ 0, y ≥ 0, z ≥ 0. and