Use parametric linear programming to find an optimal solution for the following problem as a function of

, for 0 30.

Maximize Z(

)  5x1  6x2  4x3  7x4, subject to 3x1  2x2  x3  3x4 135  2 2x1  4x2  x3  2x4 78 

x1  2x2  x3  2x4 30 

and xj 0, for j  1, 2, 3, 4.

Then identify the value of that gives the largest optimal value of Z(

).