$1-(30$ pts$.)$ An oil refinery can buy two types of oil: light crude oil and heavy crude oil. The cost per barrel of these types is respectively $$20$ and $$15.$ The following quantities of gasoline, kerosene, and jet fuel are produced per barrel of each type of oil.

$\backslash$table$[[,$Gasoline,Kerosene,Jet Fuel$],[$Light crude Oil,$0\mathrm{.}2,0\mathrm{.}2,0\mathrm{.}35],[$Heavy Crude Oil,$0\mathrm{.}32,0\mathrm{.}4,0\mathrm{.}2]]$

Note that $5$ percent and $8$ percent, respectively, of the light and heavy crude oil are lost during the refining process. The refinery has contracted to deliver $1$ million barrels of gasoline, $500,000$ barrels of kerosene, and $300,000$ barrels of jet fuel. Formulate the problem of finding the number of barrels of each crude oil that satisfies the demand and minimizes the total cost as a linear program.