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You are the CEO of Leadership Power and Light (LPL), a shareholder-owned electric utility in Florida. One of your largest customers is the City of Gilligan's Beach, Florida, a city of about 75,000 residents in a metropolitan area of about 450,000 people. The municipality spends slightly over $1 million per year on electricity to power its streetlights. The current arrangement with the City of Gilligan's Beach is that your company owns all the streetlights in Gilligan's Beach and charges the City for fixture installation or replacement, maintenance and energy costs.
Gilligan's Beach has approached you asking that, over a period of several years, you convert all the existing streetlights from high-pressure sodium fixtures (the standard type of streetlight bulb in the U.S. for decades) to LED (Light Emitting Diode) fixtures and bulbs. The City estimates that ultimately it could save $150,000 per year in energy and labor costs from such a conversion.
You are concerned about the cost of accepting this proposal, especially since it is not clear that LPL will realize any savings or additional revenue from the conversion. (See the article below for more background on situations like this one.) On the other hand, you wish to be efficient and to reduce as much as possible the negative environmental effects of generating electricity. You are also very concerned with LPL's reputation, so you want to ensure that your decision in this situation adheres to the highest ethical standards.
Graph the constraints for this problem. Indicate all feasible solutions. Find out the optimal solution to LP Relaxation. Round down to find out a feasible integer solution. Is this solution optimal?
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