PROBLEMS
Note:
The following problems have been designed to give you an understanding and apprecia
tion of the broad range of problems that can be formulated as linear programs. You should be
able to formulate a linear programming model for each of the problems. However, you will need
access to a linear programming computer package to develop the solutions and make the re
quested interpretations.
1.
The Westchester Chamber of Commerce periodically sponsors public service seminars and
programs. Currently, promotional plans are under way for this year's program. Advertis
ing alternatives include television, radio, and newspaper. Audience estimates, costs, and
maximum media usage limitations are as shown.
Constraint
Television
Radio
Newspaper
Audience per advertisement
100,000
1 8,000
40,000
Cost per advertisement
$2000
$300
$600
Maximum media usage
10
20
10
To ensure a balanced use of advertising media, radio advertisements must not exceed 50%
of the total number of advertisements authorized. In addition, television should account for
at least 10% of the total number of advertisements authorized.
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View Full DocumentProblems
195
a.
If the promotional budget is limited to $18,200, how many commercial messages
should be run on each medium to maximize total audience contact? What is the allo
cation of the budget among the three media, and what is the total audience reached?
b.
By how much would audience contact increase if an extra $100 were allocated to the
/
promotional budget?
2.
The management of Hartman Company is trying to determine the amount of each of two
products to produce over the coming planning period. The following information concerns
labor availability, labor utilization, and product profitability.
Department
A
B
C
Profit contributionlunit
Product (hoursfunit)
LaborHours
Available
100
36
50
a.
Develop a linear programming model of the Hartman Company problem. Solve the
model to determine the optimal production quantities of products 1 and 2.
In computing the profit contribution per unit, management doesn't deduct labor costs
because they are considered fixed for the upcoming planning period. However, sup
pose that overtime can be scheduled in some of the departments. Which departments
would you recommend scheduling for overtime? How much would you be willing to
pay per hour of overtime in each department?
c.
Suppose that 10,6, and 8 hours of overtime may be scheduled in departments A, B, and
C, respectively. The cost per hour of overtime is $18 in department
A,
$22.50 in de
partment B, and $12 in department
C.
Formulate a linear programming model that can
be used to determine the optimal production quantities if overtime is made available.
What are the optimal production quantities, and what is the revised total contribution
to profit? How much overtime do you recommend using in each department? What is
the increase in the total contribution to profit if overtime is used?
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 Spring '09
 shakroh
 Math, Linear Programming, linear programming model

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