Solve the follwoing linear program using Excel Solver. Consider X$,$ Y$,$ and Z are the units of three products to be produced in order to maximize total profit, and the constraints represent the capacity available at three prodution departments, C$1,$ C$2,$ and C$3,$ where all products must be processed.

Max $7$X $+2$Y$+5$Z

s$.$t$.$

$($C$1)$ X $+2$Y $+$ Z $<=25$

$($C$2)$ X $+4$Y $+2$Z $<=40$

$($C$3)3$X $+3$Y $+$ Z $<=30$

X$,$ Y$,$ Z $>=0$

$(1)$ Optimal solution $($X$,$ Y$,$ Z$)=(,,),$ and

$(2)$ the corresponding objective function value $=$

Assume product X has become outdated and the company decided to terminate this product line $($left with products Y and Z$).$ Also assume resources availability at departments C$1,$ C$2,$ C$3,$ and consumption rate for the two remaining products at the three departments stay the same.

$(3)$ What is the new optimal solution after dropping product X$?($Y$,$ Z$)=(,)$

$(4)$ The corresponding objective function value $=$