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Please Solve RD Sharma Class 12 Chapter 29 Linear Programming Exercise 29.4 Question 8 Maths Textbook Solution.

Answers (1)

Answer:

Output is maximum when type A = 4, type B = 3 or type A = 6, type B = 0.

Hint:

Let required number of machine A and B are x and y.

Given:

Production of each machine A and B are 60 and 40 units daily.

Solution:

Let z donate total output daily, so

$z=60x+40y$

Since each machine of type A and type B require 100sq.m and 1200sq.m but total area available for machine is 76000sq.m

$1000x+1200y\leq 7600$

$5x+6y\leq 38$

Each machine of type A and B require 12 men and 8 men to work respectively. But total 72 men available for work so

$\begin{aligned} &12 x+8 y \leq 72 \\ & \end{aligned}$

$3 x+2 y \leq 18$

The required LPP is

Max $z=60x+40y$

Subject to constraints

$5x+6y\leq 38$

$3x+2y\leq 18$

$x,y\geq 0,$
The feasible region obtains by the system of constraint

P(4,3) is obtain by solving (i) and (ii).

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

Corner Points	Value of $z=60x+40y$
$O\left ( 0,0 \right )$	$0$
$A_{2}(6,0)$	$360$
$P(4,3)$	$360$
$B_{1}(0,193)$	$760/3$

Therefore, max z=360 at x=4, y=3 or x=6, y=20.

Output is maximum when 4 machine of type A and 3 machines of type B or 6 machine of type A and no machine of type B.

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