Concept explainers
The objective function and the constraint equations for minimizing the transportation cost for the community.
Answer to Problem 3.16P
The objective function for minimizing the transportation cost for the community is
The constraint equations are
Explanation of Solution
Given:
The community is shown in the figure below:
Figure (1)
Assume that the cost of disposal is the same at both the disposal sites, and therefore, the disposal cost can be ignored.
Write the expression for the general objective equation for transportation cost.
Here, the transportation cost is
In Figure-(1) there are three routes, this means there are three sources and two disposal sites A and B.
Substitute
From the given data disposal cost can be ignored.
Thus, expand the above equation to find the transportation cost.
Write the
The waste hauled is equal to or less than the capacity of the disposal sites.
Here, the disposal site is
Expand Equation (II) to find the
Write the
The waste hauled is equal to the capacity of the disposal sites.
Here, the disposal site is
Expand Equation (III) to find the
The quantity of the waste hauled out must be positive.
Conclusion:
Thus, the objective function for minimizing the transportation cost for the community is
The constraint equations are
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