A company manufactures $3$ products A$,$ B and C$,$ which sells Rs$.14,$ Rs$.15$ and Rs$.22$ per unit respectively. These prices are constant and independent of the market state they are addressed to$,$ and it is also supposed that any produced quantity can be sold. For the manufacturing of these products four types of raw materials are required. The prices of raw materials, the raw material units needed for each product type and the corresponding available quantities within a certain time are included in the following table. Please share the step by step calculation and explanation

Note$-$ Read Unit price as Rs$.$ In the table given below

$\backslash$table$[[\backslash$table$[[$Raw$],[$material$]],\backslash$table$[[$Unit price$],[()]],$Products,$\backslash$table$[[$Available raw$],[$material units$]]],[,$a$,$b$,$c$,],[1,3,0,2,3,50],[2,2,3,2,1,200],[3,0\mathrm{.}5,4,4,6,200],[4,1,0,0,2,100]]$

The company's goal is to determine the quantities of each product which should be produced to achieve the highest profit. Calculate the profit and all constraints of the problem. Please share the step by step calculation and explanation.