Q$2$

A manufacturing firm produces two different products from two main raw materials. Producing one unit of product $1$ requires $2kg$ of row material $1$ and $1kg$ of row material $2.$ One unit of product $2$ requires $3kg$ of row material $1$ and $2kg$ of row material $2.$ The firm currently has $12kg$ of row material $1$ and $8kg$ of row material $2$ available in the stock for the next week. According to the market study, the firm estimates the weekly demand for product $1$ to be not more than $5$ units, while no restriction related to amount to be produced about product $2.$ Formulate a linear programming model that maximizes the profit given that the fim gains a marginal profit of $$2$ per unit of product $1$ and $$3$ per unit of product $2.$ With graph