The solution set of the linear programming, Maximize 16 x + 14 y subject to the constraints, { 10 x + 8 y ≤ 3600 5 x + 3 y ≤ 1498 6 x + 8 y ≤ 2396 x ≥ 0 , y ≥ 0 using simplex method.

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Answer 1

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Chapter 4, Problem 3P

To determine

To calculate: The solution set of the linear programming,

Maximize 16x+14y subject to the constraints,

{10x+8y≤36005x+3y≤14986x+8y≤2396x≥0,y≥0

using simplex method.

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Suppose we have a linear program in standard equation form maximize cTx subject to Ax = b. x ≥ 0. and suppose u, v, and w are all optimal solutions to this linear program. (a) Prove that zu+v+w is an optimal solution. (b) If you try to adapt your proof from part (a) to prove that that u+v+w is an optimal solution, say exactly which part(s) of the proof go wrong. (c) If you try to adapt your proof from part (a) to prove that u+v-w is an optimal solution, say exactly which part(s) of the proof go wrong.

a) Suppose that we are carrying out the 1-phase simplex algorithm on a linear program in standard inequality form (with 3 variables and 4 constraints) and suppose that we have reached a point where we have obtained the following tableau. Apply one more pivot operation, indicating the highlighted row and column and the row operations you carry out. What can you conclude from your updated tableau? x1 x2 x3 81 82 83 84 81 -2 0 1 1 0 0 0 3 82 3 0 -2 0 1 2 0 6 12 1 1 -3 0 0 1 0 2 84 -3 0 2 0 0 -1 1 4 -2 -2 0 11 0 0-4 0 -8

Microsoft Excel snapshot for random sampling: Also note the formula used for the last column 02 x✓ fx =INDEX(5852:58551, RANK(C2, $C$2:$C$51)) A B 1 No. States 2 1 ALABAMA Rand No. 0.925957526 3 2 ALASKA 0.372999976 4 3 ARIZONA 0.941323044 5 4 ARKANSAS 0.071266381 Random Sample CALIFORNIA NORTH CAROLINA ARKANSAS WASHINGTON G7 Microsoft Excel snapshot for systematic sampling: xfx INDEX(SD52:50551, F7) A B E F G 1 No. States Rand No. Random Sample population 50 2 1 ALABAMA 0.5296685 NEW HAMPSHIRE sample 10 3 2 ALASKA 0.4493186 OKLAHOMA k 5 4 3 ARIZONA 0.707914 KANSAS 5 4 ARKANSAS 0.4831379 NORTH DAKOTA 6 5 CALIFORNIA 0.7277162 INDIANA Random Sample Sample Name 7 6 COLORADO 0.5865002 MISSISSIPPI 8 7:ONNECTICU 0.7640596 ILLINOIS 9 8 DELAWARE 0.5783029 MISSOURI 525 10 15 INDIANA MARYLAND COLORADO

Answer 2

Question

Chapter 4, Problem 3P

To determine

To calculate: The solution set of the linear programming,

Maximize 16x+14y subject to the constraints,

{10x+8y≤36005x+3y≤14986x+8y≤2396x≥0,y≥0

using simplex method.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 4, Problem 3P

To determine

To calculate: The solution set of the linear programming,

Maximize 16x+14y subject to the constraints,

{10x+8y≤36005x+3y≤14986x+8y≤2396x≥0,y≥0

using simplex method.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 4, Problem 3P

To determine

To calculate: The solution set of the linear programming,

Maximize 16x+14y subject to the constraints,

{10x+8y≤36005x+3y≤14986x+8y≤2396x≥0,y≥0

using simplex method.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 4, Problem 3P

To determine

To calculate: The solution set of the linear programming,

Maximize 16x+14y subject to the constraints,

{10x+8y≤36005x+3y≤14986x+8y≤2396x≥0,y≥0

using simplex method.

Answer 6

Chapter 4, Problem 3P

To determine

To calculate: The solution set of the linear programming,

Maximize 16x+14y subject to the constraints,

{10x+8y≤36005x+3y≤14986x+8y≤2396x≥0,y≥0

using simplex method.

Answer 7

Chapter 4, Problem 3P

To determine

To calculate: The solution set of the linear programming,

Maximize 16x+14y subject to the constraints,

{10x+8y≤36005x+3y≤14986x+8y≤2396x≥0,y≥0

using simplex method.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 4.1 - 1. Determine by inspection a particular solution...Ch. 4.1 - Prob. 2CYU Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - 712For each of the linear programming problems in...Ch. 4.1 - 7–12 For each of the linear programming problems...

The solution set of the linear programming, Maximize 16 x + 14 y subject to the constraints, { 10 x + 8 y ≤ 3600 5 x + 3 y ≤ 1498 6 x + 8 y ≤ 2396 x ≥ 0 , y ≥ 0 using simplex method.

Solution Summary: The author explains the simplex method used to solve linear programming problems. The number of St. Nick and Holly assortments is 218 and 136 respectively.

Videos

To calculate: The solution set of the linear programming,

Maximize 16x+14y subject to the constraints,

{10x+8y≤36005x+3y≤14986x+8y≤2396x≥0,y≥0

using simplex method.

Want to see the full answer?

Chapter 4 Solutions

The solution set of the linear programming, Maximize 16 x + 14 y subject to the constraints, { 10 x + 8 y ≤ 3600 5 x + 3 y ≤ 1498 6 x + 8 y ≤ 2396 x ≥ 0 , y ≥ 0 using simplex method.

Solution Summary: The author explains the simplex method used to solve linear programming problems. The number of St. Nick and Holly assortments is 218 and 136 respectively.

Videos

To calculate: The solution set of the linear programming, Maximize 16x+14y subject to the constraints, {10x+8y≤36005x+3y≤14986x+8y≤2396x≥0,y≥0 using simplex method.

Want to see the full answer?

Chapter 4 Solutions

To calculate: The solution set of the linear programming,

Maximize 16x+14y subject to the constraints,

{10x+8y≤36005x+3y≤14986x+8y≤2396x≥0,y≥0

using simplex method.