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(solution) Hello, I need help with this questions.. 1) integer LP problem.


Hello, I need help with this questions.. 

1) integer LP problem.

The football boosters club for Bellevue has planned a 2-day fund-raising 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

$16

$33

6

13

Night

17

37

7

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 pro­gramming model for this problem.

Define the decision variables:

Define the objective function(Z):

c) Define the constraints:

  • Solve and report the optimal solution here (Z and values for all decision variables)

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 5. Georgia Supply (1,000 tons)

What is the total supply? _____________

What is the total Demand? _____________Is this a balanced or an unbalanced model? ____________What is the difference between a balanced and an unbalanced model? Define the objective function(Z):Define the constraints:Determine the optimal shipments from farms to plants to distribution centers to minimize total transportation costs.

Draw the diagram:

 


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