@@ -1102,6 +1102,8 @@ x_1 \geq 0, \quad x_2 \geq 0
11021102
11031103### - [ ** Objective:** ] ( ) :
11041104
1105+ <br >
1106+
11051107$Z = 4x_1 + 3x_2$
11061108
11071109<br >
@@ -1112,7 +1114,9 @@ Z = 4x_1 + 3x_2
11121114
11131115<br >
11141116
1115- ### ➢ [ ** Subject to:** ] ( ) :
1117+ ### - [ ** Subject to:** ] ( ) :
1118+
1119+ <br >
11161120
11171121$$
11181122\begin{cases}
@@ -1124,6 +1128,8 @@ x_1 \geq 0, \quad x_2 \geq 0
11241128\end{cases}
11251129$$
11261130
1131+ <br >
1132+
11271133``` latex
11281134\begin{cases}
11291135x_1 + 3x_2 \leq 7 \\
@@ -1142,7 +1148,7 @@ Convert inequalities into equalities to draw the lines:
11421148
11431149<br >
11441150
1145- ### [ 1] ( ) . $x_1 + 3x_2 = 7$
1151+ ### [ 1] ( ) : $x_1 + 3x_2 = 7$
11461152 - If $x_1 = 0 \Rightarrow x_2 = \frac{7}{3} \approx 2.33$
11471153 - If $x_2 = 0 \Rightarrow x_1 = 7$
11481154
@@ -1156,7 +1162,7 @@ x_1 + 3x_2 = 7$
11561162
11571163<br >
11581164
1159- ### [ 2] ( ) . $2x_1 + 2x_2 = 8$
1165+ ### [ 2] ( ) : $2x_1 + 2x_2 = 8$
11601166 - If $x_1 = 0 \Rightarrow x_2 = 4$
11611167 - If $x_2 = 0 \Rightarrow x_1 = 4$
11621168
@@ -1170,7 +1176,7 @@ x_1 + 2x_2 = 8
11701176
11711177<br >
11721178
1173- ### [ 3] ( ) . $x_1 + x_2 = 3$
1179+ ### [ 3] ( ) : $x_1 + x_2 = 3$
11741180 - If $x_1 = 0 \Rightarrow x_2 = 3$
11751181 - If $x_2 = 0 \Rightarrow x_1 = 3$
11761182
@@ -1184,7 +1190,7 @@ x_1 + x_2 = 3
11841190
11851191<br >
11861192
1187- ### [ 4] ( ) . $x_2 = 2$ → horizontal line
1193+ ### [ 4] ( ) : $x_2 = 2$ → horizontal line
11881194
11891195<br >
11901196
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