Solve {l}{text{imize}Z=12x_{1}+20x}{text{jecttotheconstraint}}{{l}{6x_{1}+8x_{2}>=100}{7x_{1}+12x_{2}>=120}}

$$\left. \begin{array} { l } { \text { imize } Z = 12 x _ { 1 } + 20 x } \\ { \text { ject to the constraint } } \\ { \left. \begin{array} { l } { 6 x _ { 1 } + 8 x _ { 2 } > = 100 } \\ { 7 x _ { 1 } + 12 x _ { 2 } > = 120 } \end{array} \right. } \end{array} \right.$$

Solve for x

$$x=\frac{Z-12x_{1}}{20}$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$12x_{1}+20x=Z$$

Subtract 12x_{1} from both sides.

$$20x=Z-12x_{1}$$

Divide both sides by 20.

$$\frac{20x}{20}=\frac{Z-12x_{1}}{20}$$

Dividing by 20 undoes the multiplication by 20.

$$x=\frac{Z-12x_{1}}{20}$$

Divide Z-12x_{1} by 20.

$$x=\frac{Z}{20}-\frac{3x_{1}}{5}$$