Kalyan Singhal Corp. makes three products, and it has three machines available as resources as given in the following LP problem: Maximize contribution = 6X₁ +8X2 +4X3 1X₁ +7X2 +4X3 ≤ 72 (C₁ hours on machine 1) 2X1 + 1X2 +7X3 ≤ 76 8X1 + 4X2 + 1X3 ≤ 72 (C2: hours on machine 2) (C3: hours on machine 3) X1, X2, X3 ≥0 a) Using a computer software for solving LP, the optimal solution achieved is: X₁ = 5.64 (round your response to two decimal places). X24.57 (round your response to two decimal places). X3 = 8.59 (round your response to two decimal places). Contribution (objective value) = 104.77 (round your response to two decimal places). b) Machine 1 has 0 hours of unused time available at the optimal solution (round your response to two decimal places). Machine 2 has 0 hours of unused time available at the optimal solution (round your response to two decimal places). Machine 3 has 0 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 .64 dollars to the firm (round your response to two decimal places). d) An additional 5 hours of time available for the second machine, at no cost to the firm, are going to increase the objective value by response to two decimal places). dollars (round your
Kalyan Singhal Corp. makes three products, and it has three machines available as resources as given in the following LP problem: Maximize contribution = 6X₁ +8X2 +4X3 1X₁ +7X2 +4X3 ≤ 72 (C₁ hours on machine 1) 2X1 + 1X2 +7X3 ≤ 76 8X1 + 4X2 + 1X3 ≤ 72 (C2: hours on machine 2) (C3: hours on machine 3) X1, X2, X3 ≥0 a) Using a computer software for solving LP, the optimal solution achieved is: X₁ = 5.64 (round your response to two decimal places). X24.57 (round your response to two decimal places). X3 = 8.59 (round your response to two decimal places). Contribution (objective value) = 104.77 (round your response to two decimal places). b) Machine 1 has 0 hours of unused time available at the optimal solution (round your response to two decimal places). Machine 2 has 0 hours of unused time available at the optimal solution (round your response to two decimal places). Machine 3 has 0 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 .64 dollars to the firm (round your response to two decimal places). d) An additional 5 hours of time available for the second machine, at no cost to the firm, are going to increase the objective value by response to two decimal places). dollars (round your
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
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Transcribed Image Text:Kalyan Singhal Corp. makes three products, and it has three machines available as resources as given in the following LP
problem:
Maximize contribution =
6X₁ +8X2 +4X3
1X₁ +7X2 +4X3 ≤ 72
(C₁ hours on machine 1)
2X1 + 1X2 +7X3 ≤ 76
8X1 + 4X2 + 1X3 ≤ 72
(C2: hours on machine 2)
(C3: hours on machine 3)
X1, X2, X3 ≥0
a) Using a computer software for solving LP, the optimal solution achieved is:
X₁ = 5.64 (round your response to two decimal places).
X24.57 (round your response to two decimal places).
X3 = 8.59 (round your response to two decimal places).
Contribution (objective value) = 104.77 (round your response to two decimal places).
b) Machine 1 has 0 hours of unused time available at the optimal solution (round your response to two decimal places).
Machine 2 has 0 hours of unused time available at the optimal solution (round your response to two decimal places).
Machine 3 has 0 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 .64 dollars to the firm (round your response to two decimal places).
d) An additional 5 hours of time available for the second machine, at no cost to the firm, are going to increase the objective value by
response to two decimal places).
dollars (round your
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