Explanation Given Information: Minimize c = − x + 2 y subject to the given following constraint y ≤ 2 x 3 , x ≤ 3 y , x + y ≤ 16 and x ≥ 6 , y ≥ 4 . Formula used: The steps for Linear Programming problems: 1. Draw a rectangle large enough that all the corner points are inside the rectangle. 2. Shade the outside of the rectangle so as to define a new bounded feasible region and locate the new corner points. 3. Obtain the optimal solutions using bounded feasible region. 4. If the optimal solution occurs at the one of the corner points, then LP problem has that corner point as optimal solution otherwise it has no optimal solution. Calculation: Consider the first constraint equation, y = 2 x 3 To plot the graph of the function, find the ordered pairs of the equation by substituting different values of x . For x = 0 , substitute 0 for x , y = 2 3 ⋅ 0 = 0 For x = 3 , substitute 3 for x , y = 2 3 ⋅ 3 = 2 ⋅ 1 = 2 For x = 6 , substitute 6 for x , y = 2 3 ⋅ 6 = 2 ⋅ 2 = 4 Construct a table for the ordered pairs, x 0 3 6 y 0 2 4 Test the first inequality by ( 1 , 1 ) test coordinates. y ≤ ? 2 x 3 1 ≤ ? 2 3 ⋅ 1 1 ≤ 2 3 The inequality is not satisfied. If the test point does not satisfy the inequality then the set of solutions is the line plus the entire region on the other side of the line i.e. away from the test coordinate ( 0 , 0 ) . Consider the second constraint equation. x = 3 y Isolate the variable y , by dividing both sides by 3, x = 3 y x 3 = 3 y 3 y = x 3 To plot the graph of the function, find the ordered pairs of the second constraint equation by substituting different values of x . For x = 0 , substitute 0 for x , y = 0 3 = 0 For x = 3 , substitute 3 for x , y = 3 3 = 1 For x = 6 , substitute 6 for x , y = 6 3 = 2 Construct a table for the ordered pairs of second constraint equation, x 0 3 6 y 0 1 2 Test the second inequality by (1, 1) test coordinates. x ≤ ? 3 y 1 ≤ ? 3 ⋅ 1 1 < 3 The inequality is satisfied. If the test point satisfies the inequality then the set of solutions is the line plus the entire region on the same side of the line as the test coordinate ( 1 , 1 ) . Consider the third constraint equation. x + y = 16 Isolate the variable y , by subtracting x from both sides, x − x + y = 16 − x y = 16 − x To plot the graph of the function, find the ordered pairs of the third constraint equation by substituting different values of x . For x = 0 , substitute 0 for x , y = 16 − 0 = 16 For x = 1 , substitute 1 for x , y = 16 − 1 = 15 For x = 2 , substitute 2 for x , y = 16 − 2 = 14 Construct a table for the ordered pairs of third constraint equation, x 0 1 2 y 16 15 14 Test the third inequality by (0, 0) test coordinates. x + y ≤ ? 16 0 + 0 ≤ ? 16 0 < 16 The inequality is satisfied. If the test point satisfies the inequality then the set of solutions is the line plus the entire region on the same side of the line as the test coordinate ( 0 , 0 ) Consider the fourth constraint equation. x = 6 There is straight line passing through ( 6 , 0 )

Bundle: Finite Mathematics, 7th + WebAssign Printed Access Card for Waner/Costenoble's Finite Mathematics, 7th Edition, Single-Term

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ISBN: 9781337604956

Author: Waner

Publisher: CENGAGE L

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Chapter 5.2, Problem 22E

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To calculate: The optimal solution of given linear programming problem to minimize c=−x+2y subject to the given following constraints y≤2x3, x≤3y, x+y≤16 and x≥6,y≥4.

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Chapter 5.2, Problem 21E

Chapter 5.2, Problem 23E

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Bundle: Finite Mathematics, 7th + WebAssign Printed Access Card for Waner/Costenoble's Finite Mathematics, 7th Edition, Single-Term

Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - Prob. 6E Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - Prob. 9E Ch. 5.1 - In Exercises 1-26, sketch the region that...

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The optimal solution of given linear programming problem to minimize c = − x + 2 y subject to the given following constraints y ≤ 2 x 3 , x ≤ 3 y , x + y ≤ 16 and x ≥ 6 , y ≥ 4 .

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To calculate: The optimal solution of given linear programming problem to minimize c=−x+2y subject to the given following constraints y≤2x3, x≤3y, x+y≤16 and x≥6,y≥4.

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