UEMT 3113 Operations research and
optimization
Tutorial #2
1.
The advertising alternatives for a company include television, radio, and newspaper
advertisements. The costs and estimates of audience coverage are provided in Table
below:
Cost per advertisement
Audience per advertisement
Television
$ 2000
100,000
Newspaper
$ 600
40,000
Radio
$ 300
18,000
The local newspaper limits the number of weekly advertisements from a single
company to ten. Moreover, in order to balance the advertising among the three types
of media, no more than half of the total number of advertisements should occur on
the radio, and at least 10% should occur on television. The weekly advertising budget
is $ 18,200. How many advertisements should be run in each of the three types of
media to maximize the total audience?
2.
A manufacturer produces three models of bicycles. The times (in hours) required for
assembling, painting, and packaging each model are shown in the table below.
Model A
2
1.5
1
Assembling
Painting
Packaging
Model B
2.5
2
0.75
Model C
3
1
1.25
The total times available for assembling, painting, and packaging are 4006 hours,
2495 hours, and 1500 hours, respectively. The profits per unit for the three models
are $45 (model A), $50 (model B), and $55 (model C). How many of each type
should be produced to obtain a maximum profit?
3.
Minimize Z = 5x1 – 4x2 + 6x3 – 8x4
x1 + 2x2 + 2x3 + 4x4  40
2x1 - x2 + x3 + 2x4  8
4x1 – 2x2 + x3 – x4  10
x1, x2, x3, x4  0
4.
An automobile company has two factories. One factory has 400 cars (of a certain
model) in stock and the other factory has 300 cars (of the same model) in stock. Two
customers order this car model. The first customer needs 200 cars, and the second
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customer needs 300 cars. The costs of shipping cars from the two factories to the
customers are shown in Table below.
Factory 1
Factory 2
Customer 1
$ 30
$ 36
Customer 2
$ 25
$ 30
How should the company ship the cars in order to minimize the shipping costs?
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