Solve the following linear programming problem graphically.Minimi… - Vidyadip

Question

Solve the following linear programming problem graphically.Minimise $\text{z = 3x + 5y}$
subject to the constraints
$\text{x + 2y}\geq 10$
$\text{x + y}\geq 6$
$\text{3x + y}\geq 8$
$\text{x, y}\geq 0.$

✓

Answer

Vertices are A (10, 0), 2, 4 ), C(1, 5) & D (0, 8)$\text{Z = 3 x + 5y}$ is minimum
at B (2, 4) and the minimum Value is 26.
on Ploting $\text{(3x + 5y < 26)}$
since these it no common point with the feasible
region, Hence, $\text{x = 2, y = 4}$ gives minimum Z

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Linear Programming→Linear Programming — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Differentiate the following functions with respect to x:
$\cos^{-1}\Big\{\frac{\text{x}}{\sqrt{\text{x}^2+\text{a}^2}}\Big\}$

If $\begin{bmatrix}\text{x}&4&1\end{bmatrix}\begin{bmatrix}2&1&2\\1&0&2\\0&2&-4\end{bmatrix}\begin{bmatrix}\text{x}\\4\\-1\end{bmatrix}=0,$ find x.

Solve the following initial value problems:
$\text{xe}^{\frac{\text{y}}{\text{x}}}-\text{y + x}\frac{\text{dy}}{\text{dx}}=0,\text{y(e)}=0$

Prove the following results:
$2\sin^{-1}\frac{3}{5}-\tan^{-1}\frac{17}{31}=\frac{\pi}{4}$

If $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ are non-zero, non-coplanar vectors, prove that the vector is coplanar:
$\vec{\text{a}}-2\vec{\text{b}}+3\vec{\text{c}},\ -3\vec{\text{b}}+5\vec{\text{c}}$ and $-2\vec{\text{a}}+3\vec{\text{b}}-4\vec{\text{c}}$

Evaluate the following integrals:
$\int\limits^{\pi}_0\text{x}\sin\text{x}\cos^4\text{x}\text{ dx}$

Evaluate the following integrals:
$\int^\limits1_{-1}|2\text{x}+1|\text{dx}$

Find all points of discontinuity of f, where f is defined by:
$\text {f(x)}=\begin{cases}\frac{\text x}{|\text x|},\ \ \text {if x}<0\\-1,\ \text{if x} \geq 0\end{cases}$

Solve the following differential equation:
$\frac{\text{dy}}{\text{dx}}=\text{y}\tan\text{x}-2\sin\text{x}$

Show that the function f: R → {x ∈ R: –1 < x < 1} defined by $f(\text{x})=\frac{\text{x}}{1+|\text{x}|},\text{x}\in\text{R}$ is one-one and onto function.