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Given the Following Linear Programming Problem with Two Non-Negative Variables (X1\left(X_{1}\right.

Question 51

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Given the following linear programming problem with two non-negative variables (X1\left(X_{1}\right. and X2)\left.X_{2}\right) and the range of values for the objective function coefficients that will leave the current solution optimal, answer the question that follows
Max: 50X1+75X250 X_{1}+75 X_{2}
Constraints: 2X1+5X2995X1+4X21202 X_{1}+5 X_{2} \leq 99 \quad 5 X_{1}+4 X_{2} \leq 120
Variables are non-negative
Range of values of the objective function coefficients:
30C193.7530 \leq \mathrm{C} 1 \leq 93.75
40C212540 \leq \mathrm{C} 2 \leq 125
Suppose that C1\mathrm{C} 1 is changed to 60 and C2\mathrm{C} 2 is changed to 50 simultaneously, will the same solution remain optimal?

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