Please Solve $-$ please show formulas used for excel$-$ step $by$ step. Please use data here.

Hart Manufacturing makes three products. Each product requires manufacturing operations $in$ three departments: $A,B,$ and $C.$ The labor$-$hour requirements, $by$ department, are $as$ follows.

During the next production period, the labor$-$hours available are $450in$ department $A,350in$ department $B,$ and $50in$ department $C.$ The profit contributions per unit are $$27$ for product $1,$$$29$ for product $2,$ and $$31$$ $P_f=$ units $of$ product i produced, for $i=1,2,3.P_{1^{\text{'}}},P_{2^{\text{'}}}{P}_{3}0$

$(b)$ Solve the linear program formulated $in$ part $(a).$ How much $of$ each product should $be$ produced, and what $is$ the projected total profit contribution $(in$ dollars$)?$

$(P_1,P_2,P_3)=(,)$ with profit $$1iis$ produced and zero otherwise, for $i=1,2,3.p_1,P_{2^{\text{'}}},p_{3}0$;$y_{1^{\text{'}}}{y}_2,y_3=0,1$

$(e)$ 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 $(in$ dollars$)?$