In the LPP, max Z = 15x1 + 45x2 Subject to x1 + 16x2 ≤ 250 5x1 + 2x2 ≤ 162 x2 ≤ 50 x1, x2 ≥ 0 If C2 is…

The allowable range is $15-195/16$ $\le C_1$ $\le15+195/2$, that is $45/16\le C_1\le225/2$. At the optimum the active constraints are $x_1+16x_2\le250$ and $5x_1+2x_2\le162$, with slopes $-1/16$ and $-5/2$, while the objective line has slope $-C_1/45$. Keeping the objective slope between the boundary slopes gives $1/16\le C_1/45\le5/2$.