ABC Ltd. is a medium-sized manufacturer of shelving and warehousing equipment. ABC’s products are mostly made of steel with some components made of plastic or aluminum. The manufacturing process includes different steps including cutting, pressing, and painting. In a recent meeting, the plant manager mentioned that the paint system should be the top priority of the company. The current equipment is used at full capacity and should be replaced by a system that provides greater flexibility and faster processing time, as well as a better quality of paint finishing. After some discussion, the board of the company has decided to consider the possibility of subcontracting part of the work to external firms. One such firm (External firm 1) is located 1.5km from ABC’s plant. External firm 1 has just purchased a new paint system and has excess capacity to handle the painting jobs that ABC could not do internally due to capacity constraints. ABC will have to sign a contract that guarantees a minimum volume of 60,000 m2 with external firm 1.
External firm 2, with some excess capacity, has told the plant manager that it will be willing to take some painting jobs if ABC ever needs it to.
To make a decision, the board would like you to develop a linear programming model to determine which combination of volume would minimize total painting costs. The controller has provided you with the following estimates that you should use in building your model.
Estimated annual total surface to be painted next year: 1,200,700 m2. 

The surface that cannot be outsourced due to contract restrictions or size: 

335,000 m2.
Variable costs (per m2)
Internal $ 0.15
External firm 1 0.20
External firm 2 0.18
Annual capacity (in m2)
Internal 990,000
External firm 1 300,000
External firm 2 80,000

Set up (Formulate) the linear program that will minimize the annual cost of painting for ABC.n