An Objective Function and a System of Linear Inequalities Representing $\quad \mathrm { z } = 17 \mathrm { x } - 24 \mathrm { y }$

question 10

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.
-Objective Function $\quad \mathrm { z } = 17 \mathrm { x } - 24 \mathrm { y }$
Constraints
$0 \leq \mathrm { x } \leq 5$
$0 \leq y \leq 8$
$4 x + 5 y \leq 30$
$4 x + 3 y \leq 20$

• A)Maximum: 85; at (5, 0)
• B)Maximum: 0; at (0, 0)
• C)Maximum: -98.75; at (1.25, 5)
• D)Maximum: -144; at (0, 6)

---

Definitions:

Craik And Lockhart

Refers to a theory of memory proposed by Fergus I. M. Craik and Robert S. Lockhart that suggests memory retention is determined by the depth of mental processing, with deeper levels of analysis leading to more enduring memory.

Rectangular

Having the shape or characteristics of a rectangle, which is a four-sided figure with opposing sides equal and right angles.

Long-Term Memory

The phase of the memory system capable of storing information for prolonged periods, often throughout a person's life.

Unlimited Capacity

A hypothetical concept suggesting that there's no upper limit to the amount of information the human brain can store.