Operations Research and Operations Management · Operations Research · 2 marks · Multiple choice
Maximize $Z=6x_1+5x_2$ subject to R₁: $2x_1+5x_2\le40$; R₂: $2x_1+x_2\le22$; R₃: $x_1+x_2\le13$; and x₁,x₂ ≥ 0. The optimum is (9,4). Which resource shadow prices are nonzero?
At (9,4), R₁ uses 38 of 40 and has slack, so its shadow price is zero. R₂ and R₃ are binding. Dual equalities give $2y_2+y_3=6$ and $y_2+y_3=5$, hence y₂ = 1 and y₃ = 4. Both are nonzero. **C**.
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