The solution is solved from the state and co-state equation that stationery evaluated using the indexed performance maks ? = ∫ ?(?) − ?0 ?(?) − 1 2 ?1 (?) 2 − 1 2 ?2 (?) 2? with the stationer condition that gives the optimal control ?1 ∗ = ?2?2? and ?2 ∗ = −?5?1?. The Pontryagin maximun principles is used to determine the optimal control solution. Growth liter is done by setting the intensity of light in the process of glucose formation and nutrition tofu liquid waste, tapioca, industry, and households as the additional nutrients of microalgae. This study examines mathematically the optimal control of light intensity and liquid waste nutrition in microalgae growth. This organism is a primary producer of water that has any capability to photosynthesis like any other high-level plants. The habitat of its life is in waters or humid places. Microalgae are the most primitive plant-sized cellular organisms commonly known as phytoplankton.
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