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(solution) I need help with the following 3 problems! Thank you!


I need help with the following 3 problems! Thank you! 


Problem 6 integer LP problem. The football boosters club for Bellevue has planned a 2-day fundraising drive to purchase uniforms for all the local high schools and

 

to improve facilities. Donations will be solicited during the day and

 

night by telephone and personal contact. The boosters club has

 

arranged for local college students to donate their time to solicit

 

donations. The average donation from each type of contact and the

 

time for a volunteer to solicit each type of donation are as follows:

 

Average Donation ($) Average Interview Time (min.)

 

Phone Personal

 

Phone Personal

 

Contacts Contacts

 

Contacts Contacts

 

Day

 

Night $1

 

6

 

17 $33

 

37 6

 

7 13

 

19 The boosters club has convinced several businesses and car dealers

 

to donate gasoline and cars for the college students to use to make a

 

maximum of 575 personal contacts daily during the fundraising drive.

 

The college students will donate a total of 22 hours during the day and

 

43 hours at night during the drive.

 

The president of the boosters club wants to know how many

 

different types of donor contacts to schedule during the drive to

 

maximize total donations. Formulate and solve an integer pro- gramming model for this problem.

 

a) Define the decision variables:

 

1 b) Define the objective function(Z):

 

c) Define the constraints:

 

d) Solve and report the optimal solution here (Z and values for all

 

decision variables) 2 Problem 7 Transhipment problem

 

Shafai?s Fruit Company contracts with growers in Ohio, Pennsylvania, and

 

New York to purchase grapes. The grapes are processed into juice at the

 

farms and stored in refrigerated vats. Then the juice is shipped to two

 

plants, where it is processed into bottled grape juice and frozen

 

concentrate. The juice and concentrate are then transported to three food

 

warehouses/distribution centers. The transportation costs per ton from

 

the farms to the plants and from the plants to the distributors, and the

 

supply at the farms and demand at the distribution centers are

 

summarized in the following tables:

 

Plant

 

Farm

 

4. Indiana

 

1.

 

Ohio

 

$16

 

2. Pennsylvania

 

18

 

3.

 

New York

 

22 5. Georgia

 

21

 

16

 

25 Supply (1,000 tons)

 

72

 

105

 

83 Distribution Center

 

Plant

 

6. Virginia

 

7. Kentucky

 

8. Louisiana

 

4.

 

Indiana

 

$23

 

$15

 

$29

 

5.

 

Georgia

 

20

 

17

 

24

 

Demand (1,000 tons)90

 

80

 

120

 

a) What is the total supply? _____________

 

b) What is the total Demand? _____________

 

c) Is this a balanced or an unbalanced model? ____________

 

d) What is the difference between a balanced and an unbalanced

 

model? 3 ___________________________________________________________________________

 

___________________________________________________________________________

 

__________________

 

e) Define the objective function(Z): f) Define the constraints: g) Determine the optimal shipments from farms to plants to

 

distribution centers to minimize total transportation costs.

 

h)Draw the diagram: 4 Problem 8: Assignment Problem

 

A plant has four operators to be assigned to four machines. The time

 

(minutes) required by each worker to produce a product on each

 

machine is shown in the following table:

 

Operator

 

1

 

2

 

3

 

4 A

 

10

 

5

 

12

 

8 Machine (min.)

 

B

 

C

 

D

 

12

 

9

 

11

 

10

 

7

 

8

 

14

 

13

 

11

 

15

 

11

 

9 a) Define the objective function: b) Define the constraints: c) Determine the optimal assignment and compute and report the

 

total minimum time. 5

 


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