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COMM 225 – TEST BANK SUPPLEMENTARY PROBLEMS WITH PARTIAL SOLUTION ANSWERS OF SOME OF THE PROBLEMS PART – 2 (Concordia University) 2024 $12.49
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COMM 225 – TEST BANK
SUPPLEMENTARY PROBLEMS WITH
PARTIAL SOLUTION ANSWERS OF SOME
OF THE PROBLEMS PART – 2 (Concordia
University) 2024
,SECTION 1. LINEAR PROGRAMMING FORMULATIONS
1.1) (Advertising Mix). A department store in Quebec is attempting to decide
on the types and amounts of advertising it should use. The store has invited
representatives from the local radio station, television station and newspaper to
make a presentation indicating their potential audience. The results are given as
follows.
The television station indicated that a TV commercial, which costs
$15,000, would reach 25,000 potential customers. The breakdown of the
audience is:
Male Female
Old 5,000 5,000
Young 5,000 10,000
The newspaper representative claimed an audience of 10,000 potential
customers (at a cost of $4,000) per ad, broken down as follows:
Male Female
Old 4000 3000
Young 2,000 1,000
The radio station said that the audience for one of their commercials is
15,000 customers, at a cost of $6,000. the breakdown of the customers is:
Male Female
Old 1,500 1,500
Young 4,500 7,500
The store has the following advertising policy:
1) There must be at least twice as many radio commercials as newspaper ads.
2) The campaign must reach at least 100,000 customers.
3) The store wants to reach at least twice as many young people as old.
4) At least 30% of the customers reached should be women.
Available space limits the number of newspaper ads to 7. Formulate a linear
programming model for this problem.
1.2) (Allocation Problem). A certain farming organization operates three farms
of comparable productivity. The output of each farm is limited both by the usable
acreage and by the amount of water available for irrigation. The data for the
upcoming season are the following.
Farm Usable Acreage Water
Available in
Acre Feet
1 400 1,500
1
,2 600 2,000
3 300 900
2
, The organization is considering three crops for planting which differ
primarily in their expected profit per acre and in their consumption of water.
Furthermore, the total acreage that can be devoted to each of the crops is limited
by the amount of appropriate harvesting equipment available.
Crop Maximum Water Consumption Expected
Acreage In Profit
Acre Feet Per Acre Per Acre
A 700 5 $400
B 800 4 $300
C 300 3 $100
In order to maintain a uniform workload among the farms, it is the policy of the
organization that the percentage of the usable acreage planted must be the
same at each farm. However, any combination of the crops may be grown at any
of the farms. Formulate this as a linear programming problem.
1.3) (Allocation Problem). The Clark County school district has two high
schools that serve the needs of the county. High school #1 has a student
capacity of 4,500 while high school #2 has a capacity of 2,500. The school
district is subdivided into three areas. Each area is different in size (student
population) and minority mix. The following table describes the three respective
areas:
Area Total Student Number of
Population Minority
Students
A 1,900 200
B 2,475 1,600
C 1,000 490
A court-ordered plan has been sent to the district that specifies that each high
school must have at least 32% minority enrollment. No school can have more
than 45% minority enrollment. Data indicates that the distance (miles) from each
of the areas to the respective schools are shown in the following table:
Area High School #1 High School #2
A 1.5 2.4
B 1.8 1.9
C 2.2 2.6
Busing one student costs $0.20 per mile. The district would like to avoid busing a
student more than 2.5 miles. Formulate a linear programming model that will
allow the district to meet the court-ordered plan and the busing restriction.
3
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