Kalyan Singhal Corp. makes three products, and it has three machines available a
ID: 342653 • Letter: K
Question
Kalyan Singhal Corp. makes three products, and it has three machines available as resources as given in the following LP
problem:
contribution =
5x1+4x2+3x3
1x1+7x2+4x3 is less than or equal to 90 c1: 1 hour on machine
2x1+1x1+7x3 is less than or equal to 96 c2: 2 hours on machine
8x1 + 4x2 +1x3 is less than or equal to 90 c3 three hours on machine
x1, x2, x3 is greater than or = to 0
a) Using a computer software for solving LP, the optimal solution achieved is:
Upper X 1X1equals=7.077.07
(round your response to two decimal places).
Upper X 2X2equals=5.625.62
(round your response to two decimal places).
Upper X 3X3equals=10.8910.89
(round your response to two decimal places).Contribution (objective
value)equals=90.5590.55
(round your response to two decimal places).b) Machine 1 has
00
hours of unused time available at the optimal solution (round your response to two decimal places).Machine 2 has
00
hours of unused time available at the optimal solution (round your response to two decimal places).Machine 3 has
00
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).
Enter your answer in the answer box and then click Check Answer.
*I just need help with how much an additional hour of available time for the third machine is worth. Please explain how you got it too. thanks
Maximizecontribution =
5x1+4x2+3x3
1x1+7x2+4x3 is less than or equal to 90 c1: 1 hour on machine
2x1+1x1+7x3 is less than or equal to 96 c2: 2 hours on machine
8x1 + 4x2 +1x3 is less than or equal to 90 c3 three hours on machine
x1, x2, x3 is greater than or = to 0
Explanation / Answer
Using:
1x1+7x2+4x3 is less than or equal to 90 c1: 1 hour on machine
2x1+1x1+7x3 is less than or equal to 96 c2: 2 hours on machine
8x1 + 4x2 +1x3 is less than or equal to 90 c3 three hours on machine
C.
As the binding constraint is C2, with 0.01 Hours left.
Even if we add additional hour of Machine 3 , there would not be any further production increase of X1,X2,X3.
Hence $ value of additional hour of M3 is 0.00
Max Unused C1 RHS 89.97 90 0.03 C2 RHS 95.99 96 0.01 C3 RHS 89.93 90 0.07Related Questions
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