Explanation Given Information: The given function is, f = 88 x 1 + 86 x 2 + 100 x 3 + 100 x 4 And the given inequalities are, 3 x 1 + 2 x 2 + 2 x 3 + 5 x 4 ≤ 200 2 x 1 + 2 x 2 + 4 x 3 + 5 x 4 ≤ 100 x 1 + x 2 + x 3 + x 4 ≤ 200 x 1 ≤ 40 Formula used: The following method is used, Step 1: Use different slack variables to write each constraint inequality as equation, with positive constants on the right side. Step 2: Create the simplex matrix. Step 3: Find the pivot entry. Step 4: Use row operations with only the row containing the pivot entry to make the pivot entry 1 and all other entries in the pivot column zero. Step 5: If there is negative indicator then return to step 3. If all indicators are positive or zero, an optimum value has obtained. Step 6: Set the non-basic variables equal to zero, note the values of the basic variables and the objective function from the rows of the matrix. Calculation: Consider the function f = 88 x 1 + 86 x 2 + 100 x 3 + 100 x 4 subject to: 3 x 1 + 2 x 2 + 2 x 3 + 5 x 4 ≤ 200 2 x 1 + 2 x 2 + 4 x 3 + 5 x 4 ≤ 100 x 1 + x 2 + x 3 + x 4 ≤ 200 x 1 ≤ 40 Introducing the slack variables and rewriting the objective function, 3 x 1 + 2 x 2 + 2 x 3 + 5 x 4 + s 1 = 200 2 x 1 + 2 x 2 + 4 x 3 + 5 x 4 + s 2 = 100 x 1 + x 2 + x 3 + x 4 + s 3 = 200 x 1 + s 4 = 40 − 88 x 1 − 86 x 2 − 100 x 3 − 100 x 4 + f = 0 Write this in a matrix with the objective function in the last row, x 1 x 2 x 3 x 4 s 1 s 2 s 3 s 4 f [ 3 2 2 5 1 0 0 0 0 200 2 2 ( 4 ) 5 0 1 0 0 0 100 1 1 1 1 0 0 1 0 0 200 1 0 0 0 0 0 0 1 0 40 − 88 − 86 − 100 − 100 0 0 0 0 1 0 ] Most negative value in the last row is -100 which is in two columns. So, let x 3 is the pivot column. Now divide the constants of pivot column from the last row as, 200 2 = 100 100 4 = 25 200 1 = 200 40 0 = ∞ Here 25 is the smallest quotient. So, 4 is the pivot entry. The pivot entry is shown in the matrix inside brackets. Now, multiply the Row 2 with 1 4 to get pivot entry as 1, [ 3 2 2 5 1 0 0 0 0 200 1 2 1 2 ( 1 ) 5 4 0 1 4 0 0 0 25 1 1 1 1 0 0 1 0 0 200 1 0 0 0 0 0 0 1 0 40 − 88 − 86 − 100 − 100 0 0 0 0 1 0 ] Now use operations with other rows to make all other entries in the pivot column equal to zero. So, use the following operations, Add − 2 times row 2 to row 1, add − 1 times row 2 to row 3 and add 100 times row 2 to row 5, [ 2 1 0 2.1 1 − 0

Mathematical Applications for the Management, Life, and Social Sciences

12th Edition

ISBN: 9781337625340

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

See similar textbooks

Videos

Question

Chapter 4, Problem 33RE

To determine

To calculate: The maximum value of function f=88x1+86x2+100x3+100x4 subjected to constraints 3x1+2x2+2x3+5x4≤200,2x1+2x2+4x3+5x4≤100,x1+x2+x3+x4≤200 and x1≤40.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4, Problem 32RE

Chapter 4, Problem 34RE

Students have asked these similar questions

charity savings Budget for May travel food Peter earned $700 during May. The graph shows how the money was used. What fraction was clothes? O Search Submit clothes leisure

Exercise 11.3 A slope field is given for the equation y' = 4y+4. (a) Sketch the particular solution that corresponds to y(0) = −2 (b) Find the constant solution (c) For what initial conditions y(0) is the solution increasing? (d) For what initial conditions y(0) is the solution decreasing? (e) Verify these results using only the differential equation y' = 4y+4.

SOLVE ONLY FOR (L) (M) AND (O)

Chapter 4 Solutions

Mathematical Applications for the Management, Life, and Social Sciences

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 maximum value of function f = 88 x 1 + 86 x 2 + 100 x 3 + 100 x 4 subjected to constraints 3 x 1 + 2 x 2 + 2 x 3 + 5 x 4 ≤ 200 , 2 x 1 + 2 x 2 + 4 x 3 + 5 x 4 ≤ 100 , x 1 + x 2 + x 3 + x 4 ≤ 200 and x 1 ≤ 40 .

Solution Summary: The author explains how to calculate the maximum value of the function f, which is subjected to constraints.

Videos

To calculate: The maximum value of function f=88x1+86x2+100x3+100x4 subjected to constraints 3x1+2x2+2x3+5x4≤200,2x1+2x2+4x3+5x4≤100,x1+x2+x3+x4≤200 and x1≤40.

Want to see the full answer?

Chapter 4 Solutions