An Objective Function and a System of Linear Inequalities Representing

question 14

Multiple Choice

An objective function and a system of linear inequalities representing constraints are given. Graph the system of
inequalities representing the constraints. Find the value of the objective function at each corner of the graphed
region. Use these values to determine the maximum value of the objective function and the values of x and y for
which the maximum occurs.
- $$\begin{array} { l l } \text { Objective Function } & z = 7 x - 6 y \\\text { Constraints } & x \geq 0 \\& 0 \leq y \leq 5 \\& x - y \leq 9 \\& x + 2 y \leq 12\end{array}$$

• A)Maximum: 64; at (10, 1)
• B)Maximum: 63; at (9, 0)
• C)Maximum: -16; at (2, 5)
• D)Maximum: -30; at (0, 5)

---

Definitions:

Marxist Socialists

Ideologists who follow the teachings of Karl Marx, advocating for a society without classes where the means of production are owned collectively.

Reform Socialists

Advocates a peaceful, evolutionary transition of society to socialism through legal and political reforms rather than revolutionary upheaval.

Anarchism

A political philosophy that advocates self-governed societies based on voluntary, cooperative institutions and the rejection of all involuntary, coercive forms of hierarchy.

Bakunin

Mikhail Bakunin was a Russian revolutionary anarchist, socialist and founder of collectivist anarchism.