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Please Solve RD Sharma Class 12 Chapter 29 Linear Programming Exercise 29.4 Question 9 Maths Textbook Solution.

Answers (1)

Answer:

Max profit =230 at type A=2 , type B=3.

Hint:

Let number of goods A and B are x and y respectively.

Given:

Profit of each A and B are Rs40 and Rs50

Solution:

Max $z=40x+50y$

Since each A and B require 3gm and 1gm of silver but total silver available are 9gm.

$3x+y\leq 9$

Since each A and B require 1gm and 2gm of gold but total gold available are 8gm.

$x+2y\leq 8$

The required LPP is

Max $z=40x+50y$

Subject to constraints

$\begin{aligned} &3 x+y \leq 9 \end{aligned}$

$x+2 y \leq 8 \\$

$x, y \geq 0,$

The feasible region obtains by the system of constraints

P(2,3) is obtain by solving (i) and (ii).

$OA_{1}PB_{2}$ are the shaded region

Corner Points	Value of $z=40x+50y$
$O\left (0,0 \right )$	$0$
$A_{1}(3,0)$	$120$
$P(2,3)$	$230$
$B_{2}(0,4)$	$200$

Therefore, max z=230 at x=2, y=3.

Hence maximum profit = 230, number of goods of type A =2, type B =3

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