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.)
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:
22 5. Georgia
25 Supply (1,000 tons)
83 Distribution Center
Demand (1,000 tons)90
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:
8 Machine (min.)
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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