$1.$ The manager of an oil refinery must decide on the optimal mix of two possible blending processes of which the input and output per production run are given as follows: The maximum amount available of crude $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash )$ are $200$ units and $150$ units respectively. Market requirements show that at least $100$ units of gasoline $\backslash ($ X $\backslash )$ and $80$ units of gasoline $\backslash ($ Y $\backslash )$ must be produced. The profit per production run from process $1$ and process $2$ are Rs$.300$ and Rs$.400$ respectively. Formulate this problem as a linear programming model.$|$ I