Solve the following linear programming problem graphically: Minimize: Z=5 x+10 y subject to constraints: x+2 y ≤ 120, x+y ≥ 60, x-2 y ≥ 0, x ≥ 0, y ≥…

CBSE 2023 · Region 2 · Set 1 · Q31 · 3 marks

Solve the following linear programming problem graphically : Minimize : $\displaystyle \mathrm{Z}=5 x+10 \mathrm{y}$ subject to constraints : $\displaystyle x+2 \mathrm{y} \leq 120, x+\mathrm{y} \geq 60, x-2 \mathrm{y} \geq 0$, \[x \geq 0, \quad \mathrm{y} \geq 0 \]

Linear ProgrammingLinear Programming Problem and its Mathematical FormulationApplyshort_answermedium

Corner points	Value of Z
$\displaystyle \mathbf{A}(\mathbf{4 0 , 2 0})$	$\displaystyle \mathbf{4 0 0}$
$\displaystyle \mathbf{B}(\mathbf{6 0 , 3 0})$	$\displaystyle \mathbf{6 0 0}$
$\displaystyle \mathbf{C}(\mathbf{1 2 0 , 0})$	$\displaystyle \mathbf{6 0 0}$
$\displaystyle \mathbf{D}(\mathbf{6 0 , 0})$	$\displaystyle \mathbf{3 0 0}(\mathbf{M i n})$
	$\displaystyle \mathbf{M i n}(\mathbf{Z})=\mathbf{3 0 0}$ at $\displaystyle \mathbf{x}=\mathbf{6 0} ; \mathbf{y}=\mathbf{0}$