Consider the LP: maximise $Z=5x_1+8x_2$ subject to $x_1+2x_{2}le20$ $3x_1+x_{2}le30$ $x_1,x_{2}ge0$. The optimal solution is $x_1=8,;x_2=6$. Determine the range of permissible change in the objective coefficient $c_1$ of $x_1$ such that the current solution remains optimal.

Step-by-step solution

1. Write optimal tableau at $(8,6)$ with slacks $s_1,s_2$: $x_1+2x_2+s_1=20$\n$3x_1+x_2+s_2=30$
2. Set up basis $x_1,x_2$ (since slacks positive). Compute basic solution: $x_1=8,;x_2=6,;s_1=0,;s_2=0$

Concept tested: Sensitivity analysis of objective coefficients

Published 2 September 2026 · How this solution was prepared and checked

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