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116 CHAPTER 3 LINEAR PROGRAMMING: SENSITIVITY ANALYSIS AND INTERPRETATION OF SOLUTION

TEC is now faced with the problem of establishing a strategy that will provide for
the distribution of the radios in such a way that overall profitability of the new radio
production will be maximized. Decisions must be made as to how many units should
be allocated to each of the four distribution channels, as well as how to allocate the
advertising budget and salesforce effort to each of the four distribution channels.
Problem Formulation

For the objective function, we can write:
Objective function: Maximize profit
Four constraints appear necessary for this problem. They are necessary because of
(1) a limited advertising budget, (2) limited salesforce availability, (3) a production
requirement and (4) a retail stores distribution requirement.

Constraint 1 Advertising expenditures Budget
Constraint 2 Sales time used Time available
Constraint 3 Radios produced ¼ Management requirement
Constraint 4 Retail sales Contract requirement
These expressions provide descriptions of the objective function and the constraints.
We are now ready to define the decision variables that will represent the decisions
the manager must make.
For the TEC problem, we introduce the following four decision variables:
A ¼ the number of units produced for the oil rigs market
B ¼ the number of units produced for the agriculture and forestry market
C ¼ the number of units produced for retail sales
D ¼ the number of units produced for Internet sales
Using the data in Table 3.2, the objective function for maximizing the total
contribution to profit associated with the radios can be written as follows:

Max 90A þ 84B þ 70C þ 60D
Let us now develop a mathematical statement of the constraints for the problem.
Because the advertising budget is set at $5000, the constraint that limits the amount
of advertising expenditure can be written as follows:

10A þ 8B þ 9C þ 15D 5000
Similarly, because the sales time is limited to 1800 hours, we obtain the constraint:

2A þ 3B þ 3C 1800

Management’s decision to produce exactly 600 units during the current production
period is expressed as:

A þ B þ C þ D ¼ 600
Finally, to account for the fact that the number of units distributed by the national
chain of retail stores must be at least 150, we add the constraint:

C 150
Combining all of the constraints with the nonnegativity requirements enables us to
write the complete linear programming model for the TEC problem as follows:

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