(Solution) IE 310: Operations Research HW 3 (Simplex Method) Due On Wed, Sep 21 Before Lecture Your Submision Should Have Each Problem Starting In A Fresh Page.... | Snapessays.com


(Solution) IE 310: Operations Research HW 3 (Simplex method) Due on Wed, Sep 21 before lecture Your submision should have each problem starting in a fresh page....


Consider the following problem. Maximize Z = x1 ? 7x2 + 3x3 subject to 2x1 + x2 ? x3 ? 4 4x1 ? 3x2 ? 2 ?3x1 +2x2 +x3 ?3 x1,x2,x3 ?0 (a) (points: 6) Work through the simplex method step by step to solve the problem. (b) (points: 4.5) Identify the shadow prices for the three resources and describe their significance. A group of young students earn a steady living by picking up discounted items from a used electronics store for 10$ a piece and reselling them. Each item has a street value, a weight, and a volume; there are limits on the number of available items (as shown). A total weight of 500 lbs and a total volume of 300 cu. ft. can be transported in one attempt. (a) (points: 3.5) Formulate a LP problem to find how many of each items should the students pick for reselling. 1 Item value($) weight (lbs) volume (cu. ft.) availability TV Laptop Monitor 40 50 120 30 10 20 8 5 4 20 30 15 (b) (points: 6) Solve it by the simplex method in tabular form showing the intermediate steps. 3. (Optional, no points) Consider the following problem. Maximize Z = 4x1 + 5x2 + 3x3 subject to x1 +x2 +2x3 ?20 15x1 +6x2 ?5x3 ?50 x1 +3x2 +5x3 ?30 x1,x2,x3 ?0 Work through the simplex method step by step to demonstrate that this problem does not possess any feasible solution.IE 310: Operations Research

 

HW 3 (Simplex method)

 

Due on Wed, Sep 21 before lecture

 

 

Your submision should have each problem starting in a fresh page. You should clearly state

 

the problem number. The problems should appear in order.

 

 

Write clearly. Illegible submissions will not be graded.

 

 

Staple and write your name in your submission. Unstapled/unnamed submissions will not be

 

graded.

 

 

Electronic submission will be accepted provided it is in a single ?le pdf format

 

. Submissions

 

should be through

 

Compass2g

 

. Email submissions will

 

NOT

 

be accepted.

 

 

Submission is due

 

BEFORE

 

the lecture. Strict due date will be enforced.

 

 

Collaboration and other solutions sources are

 

NOT

 

permitted.

 

1. Consider the following problem.

 

Maximize

 

Z

 

=

 

x

 

1

 

-

 

7

 

x

 

2

 

+ 3

 

x

 

3

 

subject to

 

2

 

x

 

1

 

+

 

x

 

2

 

-

 

x

 

3

 

?

 

4

 

4

 

x

 

1

 

-

 

3

 

x

 

2

 

?

 

2

 

-

 

3

 

x

 

1

 

+ 2

 

x

 

2

 

+

 

x

 

3

 

?

 

3

 

x

 

1

 

,x

 

2

 

,x

 

3

 

?

 

(a) (

 

points: 6

 

) Work through the simplex method step by step to solve the problem.

 

(b) (

 

points: 4.5

 

) Identify the shadow prices for the three resources and describe their

 

signi?cance.

 

2. A group of young students earn a steady living by picking up discounted items from a used

 

electronics store for 10$ a piece and reselling them. Each item has a street value, a weight,

 

and a volume; there are limits on the number of available items (as shown). A total weight

 

of 500 lbs and a total volume of 300 cu. ft. can be transported in one attempt.

 

Item

 

value($)

 

weight (lbs)

 

volume (cu. ft.)

 

availability

 

TV

 

40

 

30

 

8

 

20

 

Laptop

 

50

 

10

 

5

 

30

 

Monitor

 

120

 

20

 

4

 

15

 

(a) (

 

points: 3.5

 

) Formulate a LP problem to ?nd how many of each items should the

 

students pick for reselling.

 

1

 


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