A company produces two products that are processed on two assembly lines. Assembly line$1$ has $100$ available hours, and assembly line $2$ has $42$ available hours. Each product requires $10$ hours of processing time on line $1,$ while on line $2$ product $1$ requires $7$ hours and product $2$ requires $3$ hours. The profit for product $1$ is $$6$ per unit, and the profit for product $2$ is $$4$ per unit. $(5$pts$)$A$.$ Formulate a linear programming model for this problem. $($Write only objective function and constraint functions$)$