Lesson Plan 2: Hassan's Pictures - Linear Programming and Profit Lines
The questions below dealing with systems of linear inequalities have been selected from various state and national assessments. Although the lesson above may not fully equip students with the ability to answer all such test questions successfully, students who participate in active lessons like this one will eventually develop the conceptual understanding needed to succeed on these and other state assessment questions.
Taken from the Texas Assessment of Knowledge and Skills (Spring 2003):
At Northwest Electronics, audiotapes cost $5.00 per package and videotapes cost $10.00 per package. Which inequality best describes the number of packages of audiotapes, a, and the number of packages of videotapes, v that can be purchased for $45.00 or less?
A. 5a + 10v < 45
B. 10a + 5v 45 C. 5a + 10v 45 (correct answer)
D. 10a + 5v < 45
Taken from the Virginia Standards of Learning, Algebra II (Spring 2000):
This graph of a linear programming model consists of polygon ABCD and its interior. Under these constraints, at which point does the minimum value of 3x + 2y occur?