An Objective Function and a System of Linear Inequalities Representing

question 184

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.
- $$\begin{array} { l l } \text { Objective Function } & z = 7 x + 6 y \\\text { Constraints } & x \geq 0 \\& y \geq 0 \\& 3 x + y \leq 21 \\& x + y \leq 10 \\& x + 2 y \geq 12\end{array}$$

• A)Maximum 65.5; at (5.5, 4.5)
• B)Maximum 60; at (6, 3)
• C)Maximum 68; at (8, 2)
• D)Maximum 66; at (6, 4)

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Definitions:

Herfindahl-Hirschman Index

A measure of market concentration used to determine the level of competition within an industry, calculated by squaring the market share of each firm within the industry.

Oligopoly

A market structure characterized by a small number of firms dominating the market, where each has significant control over prices and supply.

Product Differentiation

The process of distinguishing a product or service from others in the market to make it more attractive to a particular target market.

Oligopoly Market

A market structure characterized by a small number of firms controlling a large majority of the market share, leading to limited competition.