Question

A manufacturer produces two types of products, 1 and 2, at production levels of $x_1\text{and}{x}_2$ respectively. The profit given is $2x_1+5x_2.$

The production constraints are:

$x_1+3x_2\le 40$

$3x_1+x_2\le 24$

$x_1+x_2\le 10$

$x_1>0$

$x_2>0$

The maximum profit which can meet the constraints is

• A. 44
• B. 50
• C. 29
• D. 75
• E. 38

Answer 1

The correct option is B 50

$\text{Given system are}$

$x_1+3x_2\le 40...\left(i\right)$
$3x_1+x_2\le 24...\left(ii\right)$
$x_1+x_2\le 10....\left(iii\right)$
$x_1>0,x_2>0$

$\text{Objective function,}$

$z=2x_1+5x_2$


$\text{Solving the eqs. (ii) and (iii); we get}$

$AtA(0,10),z_{max}=2\times 0+5\times 10=50$

$AtC(8,0),z_{max}=8\times 2+5\times 0=16$

$AtB(7,3),z_{max}=2\times 7+5\times 3=29$

$\text{So maximum value of z = 50}$