The difference in solving LPs and ILPs.

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Answer 1

Question

Chapter 6, Problem 1QP

Summary Introduction

To explain: The difference in solving LPs and ILPs.

Expert Solution & Answer

Explanation of Solution

Linear programming:

In LP problems, the optimal solutions can be any of the intersecting points of constraints in the graph within the feasible region. The optimal solution cannot be present elsewhere in the feasible region except the extreme intersection points thus making it somewhat straightforward to find the optimal solution.

When it comes to ILP problems, the optimal solution can be present at the extreme points created by the intersecting constraint in the feasible while also can be present anywhere in the feasible region. Therefore, there can be many numbers of optimal solutions for the problem. Hence, ILPs are much harder to solve than LPs.

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Consider the following primal LP problem:Maximize X1 + 2X2 – 9X3 + 8X4 – 36X5Subject to 2X2 – X3 + X4 – 3X5 ≤ 40 X1 – X2 + 2X4 – 2X5 ≤ 10 X1 ≥ 0, X2 ≤ 0, X3 ≥ 0, X4 ≥ 0, X5 ≥ 0 (a) Write the dual of the LP above, using variables Y1, Y2, etc.(b) Sketch the feasible region of the dual LP in 2 dimensions, and use the graphical method to find the dual optimalsolution (Plot an isovalue line corresponding to the feasible solution, move the line in improving direction, findthe last one touching the feasible region, and any point(s) on the intersection of the last isovalue line andfeasible region are optimal solutions)(c) Using complementary slackness conditions, - write equations which must be satisfied by the optimal primal solution X* - which primal variables must be zero?(d) Using the information in (c), determine the optimal primal solution X* (e) Compare the optimal objective values of the primal and dual solutions

For this linear programming problem, formulate the linear programming model. Then, find the optimal solution graphically for the LP with only 2 variables. i.e: Max Z = 500x + 300y Subject to: 4x + 2y <= 60 (1st constraint) 2x + 4y <= 48 (2nd constraint) x, y >= 0 (non-negativity) A construction company manufactures bags of concrete mix from beach sand and river sand. Each cubic meter of beach sand costs ₽60 and contains 4 units of fine sand, 3 units of coarse sand, and 5 units of gravel. Each cubic meter of river sand costs ₽100 and contains 3 units of fine sand, 6 units of coarse sand, and 2 units of gravel. Each bag of concrete must contain at least 12 units of fine sand, 12 units of coarse sand, and 10 units of gravel. Find the best combination of beach sand and river sand which will meet the minimum requirements of fine sand, coarse sand, and gravel at the least cost.

Consider the following LP problem with two constraints: 32X + 39Y >= 1248 and 17X + 24Y >= 408. The objective function is Max 13X + 19Y . What combination of X and Y will yield the optimum solution for this problem? a. 0 , 17 b. unbounded problem c. 0 , 17 d. infeasible problem e. 24 , 0

Answer 2

Question

Chapter 6, Problem 1QP

Summary Introduction

To explain: The difference in solving LPs and ILPs.

Expert Solution & Answer

Explanation of Solution

Linear programming:

In LP problems, the optimal solutions can be any of the intersecting points of constraints in the graph within the feasible region. The optimal solution cannot be present elsewhere in the feasible region except the extreme intersection points thus making it somewhat straightforward to find the optimal solution.

When it comes to ILP problems, the optimal solution can be present at the extreme points created by the intersecting constraint in the feasible while also can be present anywhere in the feasible region. Therefore, there can be many numbers of optimal solutions for the problem. Hence, ILPs are much harder to solve than LPs.

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Answer 3

Question

Chapter 6, Problem 1QP

Summary Introduction

To explain: The difference in solving LPs and ILPs.

Expert Solution & Answer

Explanation of Solution

Linear programming:

In LP problems, the optimal solutions can be any of the intersecting points of constraints in the graph within the feasible region. The optimal solution cannot be present elsewhere in the feasible region except the extreme intersection points thus making it somewhat straightforward to find the optimal solution.

When it comes to ILP problems, the optimal solution can be present at the extreme points created by the intersecting constraint in the feasible while also can be present anywhere in the feasible region. Therefore, there can be many numbers of optimal solutions for the problem. Hence, ILPs are much harder to solve than LPs.

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Answer 4

Question

Chapter 6, Problem 1QP

Summary Introduction

To explain: The difference in solving LPs and ILPs.

Expert Solution & Answer

Explanation of Solution

Linear programming:

In LP problems, the optimal solutions can be any of the intersecting points of constraints in the graph within the feasible region. The optimal solution cannot be present elsewhere in the feasible region except the extreme intersection points thus making it somewhat straightforward to find the optimal solution.

When it comes to ILP problems, the optimal solution can be present at the extreme points created by the intersecting constraint in the feasible while also can be present anywhere in the feasible region. Therefore, there can be many numbers of optimal solutions for the problem. Hence, ILPs are much harder to solve than LPs.

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Answer 5

Chapter 6, Problem 1QP

Summary Introduction

To explain: The difference in solving LPs and ILPs.

Expert Solution & Answer

Explanation of Solution

Linear programming:

In LP problems, the optimal solutions can be any of the intersecting points of constraints in the graph within the feasible region. The optimal solution cannot be present elsewhere in the feasible region except the extreme intersection points thus making it somewhat straightforward to find the optimal solution.

When it comes to ILP problems, the optimal solution can be present at the extreme points created by the intersecting constraint in the feasible while also can be present anywhere in the feasible region. Therefore, there can be many numbers of optimal solutions for the problem. Hence, ILPs are much harder to solve than LPs.

Answer 6

Chapter 6, Problem 1QP

Summary Introduction

To explain: The difference in solving LPs and ILPs.

Expert Solution & Answer

Explanation of Solution

Linear programming:

In LP problems, the optimal solutions can be any of the intersecting points of constraints in the graph within the feasible region. The optimal solution cannot be present elsewhere in the feasible region except the extreme intersection points thus making it somewhat straightforward to find the optimal solution.

When it comes to ILP problems, the optimal solution can be present at the extreme points created by the intersecting constraint in the feasible while also can be present anywhere in the feasible region. Therefore, there can be many numbers of optimal solutions for the problem. Hence, ILPs are much harder to solve than LPs.

Answer 7

Chapter 6, Problem 1QP

Summary Introduction

To explain: The difference in solving LPs and ILPs.

Answer 8

Expert Solution & Answer

Explanation of Solution

Linear programming:

In LP problems, the optimal solutions can be any of the intersecting points of constraints in the graph within the feasible region. The optimal solution cannot be present elsewhere in the feasible region except the extreme intersection points thus making it somewhat straightforward to find the optimal solution.

When it comes to ILP problems, the optimal solution can be present at the extreme points created by the intersecting constraint in the feasible while also can be present anywhere in the feasible region. Therefore, there can be many numbers of optimal solutions for the problem. Hence, ILPs are much harder to solve than LPs.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Ch. 6 - Prob. 1QP Ch. 6 - Prob. 3QP

The difference in solving LPs and ILPs.

Concept explainers

To explain: The difference in solving LPs and ILPs.

Explanation of Solution

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Chapter 6 Solutions