Question

Consider the following linear programming problem:

$\text{Maximize}Z=6x+10y$

$\text{Subject to :}$

$x\le 4$

$y\le 6$

$3x+2y\le 18$

$x\ge 0,y\ge 0$

The maximum value of the objective function is

• A. 72
• B. 60
• C. 54
• D. 84

Answer 1

The correct option is A 72

$\frac{X}{4}\le 1$

$\frac{Y}{6}\le 1$

$\frac{x}{6}+\frac{y}{9}\le 1$

$Z_{max}=6x+10y$

$Z(0,6)=6\times 0+10\times 6=60$

$Z(2,6)=6\times 2+10\times 6=72$

$Z(4,3)=6\times 4+10\times 3+54$

$Z_{max}=72$