Kalyan Singhal Corp. makes three products, and it has three machines available as resources as given in the following LP problem: Maximize contribution = 4X1+4X2+7X3 1X1+7X2+4X3 <= 100 2X1+1X2+7X3 <= 110 8X1+4X2+1X3 <= 100 X1,X2,X3 >=0

(a) Determine the optimal solution using LP software.

The optimal achieved is X1=

X2+

X3=

contribution =

(b) machine 1 has __ hours of unused time available at the optimal solution

machine 2 has __ hours of unused time available at the optimal solution

machine 3 has __ hours of unused time available at the optimal solution

(c) an additional hour of time available for third machine s worth __ dollars to the firm

(d) an additional 8 hours of time available for the second machine, at no cost to the firm, are going to increase the objective value by___ dollars