Larkin Industries manufactures several lines of decorative and functional metal items. The most recent order has been for 1200 door lock units for an apartment complex developer. The sales and production departments must work together to determine delivery schedules. Each lock unit consists of three components: the knob and face plate, the actual lock itself, and a set of two keys. Although the processes used in the manufacture of the three components vary, there are three areas where the production manager is concerned about the availability of resources. These three areas, their usage by the three components, and their availability are detailed in the table.
Resource Knob and Plate Lock Key (each) Available
Brass Alloy 12 5 1 15000 units
Machining 18 20 10 36000 minutes
Finishing 15 5 1 12000 minutes
A quick look at the amounts available confirms that Larkin does not have the resources to fill this contract. A subcontractor, who can make an unlimited number of each of the three components, quotes the prices below.
Component Subcontractor Cost Larkin Cost
Knob and Plate 10.00 6.00
Lock 9.00 4.00
Keys (set of 2) 1.00 .50
Develop a linear programming model that would tell Larkin how to fill the order for
1200 lock sets at the minimum cost.
The solution gives step by step procedure for the to solve a linear programing problem.