Question: The Charm City Oil Company wants to decide how to allocate its budget. The government grants certain tax breaks if the company invests funds in research concerned with energy conservation. However, the government stipulates that at least 40 percent of the funds must be funneled into research for automobile efficiency (methanol fuel research and emission reduction). The company has a budget of $2 million for investment. The research proposal data are shown in the following table.

Maximum Investment Annual Return

Project Allowed on Investment

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Methanol fuel research $600,000 2.0%

Emission reduction $450,000 2.3%

Solar cells $650,000 2.6%

Windmills $420,000 2.9%

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The company wants to receive the government tax break. How much money should be invested in each project if the company wants to maximize total annual return on its investments?

Formulate a linear programming model for the above situation.

1. Define the decision variables.
2. Determine the objective function. What does it represent?
3. Determine all the constraints. Briefly describe what each constraint represents.

Note: Do NOT solve the problem after formulating.

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