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Linear Programming / Transportation Problem : Minimizing Cost

The Widgit Company has agreed to supply its best customer with three widgits during each of the next 3 weeks, even though producing them will require some overtime work. The relevant production data are as follows:

Week Maximum Production,
Regular Time Maximum Production,
Overtime Production Cost per Unit,
Regular Time
1 2 2 $300
2 3 2 $500
3 1 2 $400

The cost per unit produced with overtime for each week is $100 more than for regular time. The cost of storage is $50 per unit for each week it is stored. There is already an inventory of two widgets on hand currently, but the company does not want to retain any widgets in inventory after the 3 weeks.
Management wants to know how many units should be produced in each week to minimize the total cost of meeting the delivery schedule.
Formulate this problem as a transportation problem by constructing the appropriate parameter table.

See attached file for full problem description.


Solution Preview

The solution is in the attached Excel file.

The first table, which shows the different production costs in each of the weeks is equivalent to the cost table from a transportation problem, in which the unit costs of transporting goods from each specific source to each specific destination are shown. In our table, ...

Solution Summary

An LP / transportation problem is solved. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.