Leary Chemical manufactures three chemicals: A$,$ B$,$ and C$.$ These chemicals are produced via two production processes: $1$ and $2.$

Running process $1$ for an hour costs $$4$ and yields $3$ units of A$,1$ of B$,$ and $1$ of C$.$

Running process $2$ for an hour costs $$1$ and produces $1$ unit of A and $1$ of B$.$

To meet customer demands, at least $10$ units of A$,5$ of B$,$ and $3$ of C must be produced daily.

Formulate a Linear Programming model and solve the problem using the graphical method or any online or commercial solvers determine a daily production plan that minimizes the cost of meeting

Leary Chemical$$s daily demands.

The details of the optimal solution are:

Number of hours of running process $1$: $\_\_\_\_\_\_\_$ Number of hours of running process $2$: $\_\_\_\_\_\_\_$ Optimum cost: $\_\_\_\_\_\_\_$