A cooperative society of farmers has 50 hecta | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $x$ hectares of land be allocated to crop $X$ and $y$ hectares to crop $Y$.Obviously,$x \geq 0, y \geq 0.$Profit per hectare on crop $X = 	ex

Vedclass · Accepted Answer

$30$ hectares for crop $X$ and $20$ hectares for crop $Y$

Vedclass · Answer

(A) Let $x$ hectares of land be allocated to crop $X$ and $y$ hectares to crop $Y$.Obviously,$x \geq 0, y \geq 0.$Profit per hectare on crop $X = 	ext{Rs } 10,500$Profit per hectare on crop $Y = 	ext{Rs } 9,000$Therefore,total profit $Z = 10,500x + 9,000y$The mathematical formulation of the problem is as follows:Maximise $Z = 10,500x + 9,000y$Subject to the constraints:$x + y \leq 50$ (constraint related to land) $... (1)$$20x + 10y \leq 800$ (constraint related to use of herbicide)i.e.,$2x + y \leq 80$ $... (2)$$x \geq 0, y \geq 0$ (non-negative constraint) $... (3)$The feasible region $OABC$ is bounded by the vertices $O(0,0), A(40,0), B(30,20),$ and $C(0,50)$.Evaluating the objective function $Z = 10,500x + 9,000y$ at these vertices:Corner Point$Z = 10,500x + 9,000y$$O(0,0)$$0$$A(40,0)$$4,20,000$$B(30,20)$$10,500(30) + 9,000(20) = 3,15,000 + 1,80,000 = 4,95,000$ (Maximum)$C(0,50)$$4,50,000$Hence,the society will get the maximum profit of Rs $4,95,000$ by allocating $30$ hectares for crop $X$ and $20$ hectares for crop $Y$.

Similar Questions

Solution of the following $LP$ problem
Minimize $z = -3x + 2y$
subject to $0 \leq x \leq 4, 1 \leq y \leq 6, x + y \leq 5$ is $.....$

For the following shaded region,the linear constraints are:

The graph with the correct feasible region of the $L.P.P.$ for the constraints $2x + y \leqslant 10$,$y \leqslant x$,$y \leqslant 2$,$x, y \geqslant 0$ is $\ldots$

The maximum value of $Z=3x+5y$,subject to the constraints $x+4y \leq 24$,$y \leq 4$,$x \geq 0$,$y \geq 0$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module