Min 8x+12Y\ s.t. \ 1x+3Y>=7\ 2x+2Y>=10\ 6x+2Y>=14\ x,y>=0

\ (a) Use the graphical solution procedure to find the optimal solution.\ What is the value of the objective function at the optimal solution?\

at (x,n)=(,)

\ (b) Assume that the objective function coefficient for

x

changes from 8 to 6 . Use the graphical solution procedure to find the new optimal solution.\ Does the optimal solution change?\ The extreme point

(x,y)=1

\ remains

optimal. The value of the objective function becomes [ solution.\ Does the optimal solution change?\ The extreme point

(x,n)=1

\ becomes

optimal. The value of the objective function becomes 4 !\ (d) The computer solution for the linear program in part (a) provides the following objective coefficient range information.\ \\\\table[[Variable,\\\\table[[Objective],[Coefficient]],\\\\table[[Allowable],[Increase]],\\\\table[[Allowable],[Decrease]]],[

x

,8.00000,4.00000,4.00000],[

Y

,12.00000,12.00000,4.00000]]

Min8X+12Ys.t.1X+3Y72X+2Y106X+2Y14X,Y0 (a) Use the graphical solution procedure to find the optimal solution. What is the value of the objective function at the optimal solution? at(x,n)=() (b) Assume that the objective function coefficient for x changes from 8 to 6 . Use the graphical solution procedure to find the new optimal solution. Does the optimal solution change? The extreme point (x,n)=() optimal. The value of the objective function becomes solution. Does the optimal solution change? The extreme point (x,n)=(x) optimal. The value of the objective function becomes (d) The ramniter solution for the linear program in part (a) provides the following objective coefficient range information