Explanation Given: The objective function to be minimized is C = x + 2 y . The constraints are, 3 x + y ≥ 12 x + 4 y ≥ 16 x ≥ 0 , y ≥ 0 Approach: (1) If all the entries are nonnegative, the optimal solution has been reached. (2) If there is one or more negative entries, the optimal solution has not been reached. Calculation: Convert the minimization problem into standard maximization problem by multiplying with negative sign. P = − C = − ( x + 2 y ) = − x − 2 y The constraint are now as, − 3 x − y ≤ − 12 − x − 4 y ≤ − 16 Introduce the slack variables, u , v in the given conditions and rewrite the objective function in the standard form that gives the system of linear equation as follows, − 3 x − y + u = − 12 − x − 4 y + v = − 16 P + x + 2 y = 0 Construct the initial simplex table. x y u v P Constant − 3 − 1 1 0 0 − 12 − 1 − 4 0 1 0 − 16 1 2 0 0 1 0 The constant in the last column are not positive. Calculate the pivot element. Let column 2 be the pivot column. x y u v P Constant Ratio − 3 − 1 1 0 0 − 12 − 12 − 1 = 12 − 1 − 4 0 1 0 − 16 − 16 − 4 = 4 1 2 0 0 1 0 The least ratio is 4 that lies in row 2 . So the pivot row is the second row. So, the element corresponding to pivot column and the pivot row is − 4 . Apply the row operation R 2 → − 1 4 R 2 in the above matrix. x y u v P Constant − 3 − 1 1 0 0 − 12 1 4 1 0 − 1 4 0 4 1 2 0 0 1 0 Apply operation R 1 → R 1 + R 2 and R 3 → R 3 − 2 R 2 . x y u v P Constant − 11 4 0 1 − 1 4 0 − 8 1 4 1 0 − 1 4 0 4 1 2 0 0 1 2 1 − 8 The element in the constant term is still not positive

Finite Mathematics for the Managerial, Life, and Social Sciences, 11th Edition

11th Edition

ISBN: 9781285464657

Author: Soo T. Tan

Publisher: Brooks Cole

See similar textbooks

Videos

Question

Chapter 4.CRE, Problem 12CRE

To determine

To find:

The solution to the minimization problem having constraints,

3x+y≥12x+4y≥16x≥0,y≥0.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.CRE, Problem 11CRE

Chapter 4.CRE, Problem 13CRE

Students have asked these similar questions

If u use any type of chatgpt, will.downvote.

A function is defined on the interval (-π/2,π/2) by this multipart rule: if -π/2 < x < 0 f(x) = a if x=0 31-tan x +31-cot x if 0 < x < π/2 Here, a and b are constants. Find a and b so that the function f(x) is continuous at x=0. a= b= 3

Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a. f(x) = (x + 4x4) 5, a = -1 lim f(x) X--1 = lim x+4x X--1 lim X-1 4 x+4x 5 ))" 5 )) by the power law by the sum law lim (x) + lim X--1 4 4x X-1 -(0,00+( Find f(-1). f(-1)=243 lim (x) + -1 +4 35 4 ([ ) lim (x4) 5 x-1 Thus, by the definition of continuity, f is continuous at a = -1. by the multiple constant law by the direct substitution property

Chapter 4 Solutions

Finite Mathematics for the Managerial, Life, and Social Sciences, 11th Edition

Ch. 4.1 - Give the three characteristics of a standard...Ch. 4.1 - a. When the initial simplex tableau is set up, how...Ch. 4.1 - In the simplex method, how is a pivoted column...Ch. 4.1 - In Exercises 1-6, a write the linear programming...Ch. 4.1 - In Exercises 1-6, a write the linear programming...Ch. 4.1 - In Exercises 1-6, a write the linear programming...Ch. 4.1 - In Exercises 1-6, a write the linear programming...Ch. 4.1 - In Exercises 1-6, a write the linear programming...Ch. 4.1 - Prob. 6E Ch. 4.1 - In Exercises 7-16, determine whether the given...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The solution to the minimization problem having constraints, 3 x + y ≥ 12 x + 4 y ≥ 16 x ≥ 0 , y ≥ 0 .

Solution Summary: The author explains how to find the solution to the minimization problem by multiplying with negative sign.

Videos

To find:

The solution to the minimization problem having constraints,

3x+y≥12x+4y≥16x≥0,y≥0.

Want to see the full answer?

Chapter 4 Solutions

The solution to the minimization problem having constraints, 3 x + y ≥ 12 x + 4 y ≥ 16 x ≥ 0 , y ≥ 0 .

Solution Summary: The author explains how to find the solution to the minimization problem by multiplying with negative sign.

Videos

To find: The solution to the minimization problem having constraints, 3x+y≥12x+4y≥16x≥0,y≥0.

Want to see the full answer?

Chapter 4 Solutions

To find:

The solution to the minimization problem having constraints,

3x+y≥12x+4y≥16x≥0,y≥0.