A company produces three types of chemical products. Products $A,B$ and $C.$ The demand for product $A$ is deterministic and equals $100$ ton every month. The demand for product $B$ is uniformly distributed with a mean of $100$ tons and lower limit of $80$ tons. The demand for product $C$ is an exponential random variable with mean $100$ tons. The sale price for a ton of product $A$ is $250$ riyals and for product $B$ is $200$ riyals and for product $C$ is $180$ riyals The raw material inputs to the production process are three types $F,G$ and $H.$ Every month the plant has $500$ tons from material $F$ and $300$ tons from material $G$ and there is no limit on the availability of material $H.$ The requirements from the materials to produce a ton of each product is given in the table below:

$\backslash$table$[[,\backslash$table$[[$Cost of$],[$material ton$]],$A$,$B$,$C$],[$Material F$,20,0\mathrm{.}4,0\mathrm{.}1,0\mathrm{.}3],[$Material G$,15,0\mathrm{.}5,0\mathrm{.}6,0\mathrm{.}4],[$Material H$,10,0\mathrm{.}3,0\mathrm{.}5,0\mathrm{.}5]]$