Larkin Industries Manufactures Several Lines of Decorative and Functional Metal

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. $$\begin{array} { l c c c c } \text { Resource } & \text { Knob and Plate } & \text { Lock } & \text { Key (each) } & \text { Available } \\\hline \text { Brass Alloy } & 12 & 5 & 1 & 15000 \text { units } \\\text { Machining } & 18 & 20 & 10 & 36000 \text { minutes } \\\text { Finishing } & 15 & 5 & 1 & 12000 \text { minutes }\end{array}$$ 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. $$\begin{array} { l c c } \text { Component } & \text { Subcontractor Cost } & \text { Larkin Cost } \\\hline \text { Knob and Plate } & 10.00 & 6.00 \\\text { Lock } & 9.00 & 4.00 \\\text { Keys (set of 2) } & 1.00 & .50\end{array}$$ Develop a linear programming model that would tell Larkin how to fill the order for 1200 lock sets at the minimum cost.