Question 11 x 1 = 0.67, x 2 = 4 , and z = 365.6 the coefficient of x 2 cannot be

Question

Question 11

x1 = 0.67, x2 = 4 , and z = 365.6

the coefficient of x2 cannot be increased by 28 as it violates the range.

x1 = 4, x2 = 0.67, and z = 372.26

none of the above

x1 = 0.67, x2 = 4 , and z = 365.6

the coefficient of x2 cannot be increased by 28 as it violates the range.

x1 = 4, x2 = 0.67, and z = 372.26

none of the above

Computer output 1 Min z 80x1 50x2 S.t. 3x1 1x126 1x1 1x2 4 2x1 6x2 212 X1,X2 20 Optimal obj Value z 353.33 Variable Value Reduced Cost 0.67 Constraint Slack and Surplus Dual Value 6.67 63.33 8.33 Variable Obi. Coefficient Allowable Allowable Increase Decrease 80 63.33 1E+ 30 50 190 50 Allowable Allowable RHS Value Constraint Increase Decrease 6.67 1E+ 30 2.5 12 1E+30

Explanation / Answer

If we see from output, the allowable increase for x2 is 190. So, till we increase x2 by 190 the optimal solution wont change.

Here, 28 lies in the range and thus optimal solution wont change.

Thus,

x1 = 4, x2 = 0.67,

Now Z = 80x1 + 50x2

becomes Z = 80x1 + 78x2

So, 80 *4 + 78 * 0.67 = 372.26

C option.

x1 = 4, x2 = 0.67,

Now Z = 80x1 + 50x2

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