Intermediate control on the subject of \"Business mathematics\", Variant 30 maximum score: 20
1. Solve the problem using graphical method.
$2x_1 + x_2 \le 10$,
$x_1 + x_2 \ge 3$,
$x_1 + x_2 \le 7$.
$6x_1 - x_2 \le 6$,
$x_1 \ge 0$; $x_2 \ge 0$,
$F = 2x_1 + 5x_2 \to \text{max}$
2. Explore on extremum $z = e^2(x + y^2)$. min = ? max = ?
3. Solve the optimization problem using Lagrange method: $z = x^2 + 2y^2$, $3x + 2y = 4$.
4. Solve the problem using dual simplex method:
$3x_1 + x_2 \ge 9$,
$x_1 + 2x_2 \ge 8$,
$x_1 + 6x_2 \ge 12$,
$x_1 \ge 0, x_2 \ge 0$,
$F = 4x_1 + 6x_2 \to \text{min}$.
