Problem $2$A factory produces two different products $($products $1$ and $2).$ Each product requires other parts tobe installed with it $($part A and B$).$ Each piece of product $1$ requires $1$ piece of part A and $2$ piecesof part B$.$ Each piece of product $2$ requires $3$ pieces of part A and $2$ pieces of part B$.$ The factoryhas $200$ pieces available of part A and $300$ pieces of part B$.$ Each piece of product $1$ generates aprofit of $$1,$ while $$2$ for product $2.$ If more than $60$ pieces of product $2$ are produced, no profit canbe generated. How many pieces of each product must be produced to maximize the profit?