Please provide Handwritten answer.

Calculus

An oil refinery has two sources of crude oil: light crude, which costs $ 35 a barrel, and heavy crude at $ 30 a barrel. With each barrel of light crude, the refinery produces 0.3 barrels of gasoline (G), 0.2 barrels of heating fuel (C) and 0.3 barrels of turbine fuel (T), while with each barrel of heavy crude it produces 0.3 barrels of G, 0.4 barrels of C and 0.2 barrels of T. The refinery has contracted the supply of 900,000 barrels of G, 800,000 barrels of C and 500,000 barrels of T. Find the quantities of light and heavy crude that you must buy in order to meet your needs at cost minimum..