Solve the mixed$-$integer linear program formulated in part $($d$).$ How much of each product should be produced and what is the projected total profit contribution? Compare this profit contribution to that obtained in part $($c$).$If required, round your answers to nearest whole number. If your answer is zero, enter $0.$

Product $1$ Product $2$ Product $3$

Amount to Produce $1001000$

Updated Profit $$\_\_\_\_\_$