Question

Kalyan Singhal Corp. makes three products, and has three machines available as resources as given in the following LP Maximize contribution contribution 6x, 8x24x X1 7X24X3 72 2x 1x2x 76 X,4X21X3 s 72 X2.X3 20 (C,: hours on machine 1) (C2: hours on machine 2) C3: hours on machine 3) a) Using a computer software for solving LP, the optimal solution achieved is: x, L] (round your response to two decrnal places). 2round your response to two decimal places) X3(round your response to two decimal places. Contribution (objective value) (round your response to two dlecimal places. b) Machine 1 has hours of unused time available at the optimal solution (round your response to two decimal places). Machine 2 hashours of unused time available at the optimal solution (round your response to two decimal places). Machine 3 has hours of unused time available at the optimal solution (round your response to two decimal places). c) An additional hour of time available for third machine, is worth dollars to the firm (round your response to two decimal places). d) An additional 10 hours of time available for the second machine, at no cost to the firm, are going to increase the objective value bydollars (round your response to two decimal places).

Answer 1

(a) using the excel we get the final iteration table

since

0 s, 1-31- 27 5-39 1-35 220-si 220-31- 0, 31 IST 스 27 1-39-32-35 14-si 프… 1-45 o s, 3-13 | 0 | 1-1.3 2. 13 10-13 10-13 5 0 0 0 4-x 0 8 3

X1 = 5.64

X2 = 4.57

X3 = 8.60

and objective function Z = 36776/351 =104.7749

b) machine 1 - 6 hr

machine 2- 8 hr

machine 3 -4 hr

c) 8.60 $