Plan for Today
• Warm Up/Stamp Homework (green WS)
• Go Over Questions from Systems of
Inequalities
• Quizzes from Friday/Monday are on-line
– Get back tomorrow
• 4.3 Notes
• 4.3 Worksheet
• Test Retakes are graded and on-line
Warm Up
Determine if the given ordered pair is a solution of
x+y≥6
x – 2y >10
1.
3.
(3, 3)
no
2.
(12, 0)
yes
4.
(10, 1)
(15, 2)
no
yes
3.4 Linear Programming
• Real Life Applications for Systems of
Inequalities
• Inequalities represent the constraints of the
problem (stipulations)
• Solution Region (Shaded region) is called the
feasible region, represents the possibilities for
the situation.
• Objective Function: How to maximize profit or
minimize cost, maximize efficiency, etc.
Working the problem (identifying the
minimum or maximum)
• Identify the variables in the problem
• Write a system of inequalities to describe the problem
• Graph the constraints (inequalities)
– Shade the feasible region
– All of these points in the feasible region are possibilities to
the problem, but not necessarily the best choice
• Identify the Objective Function
• Identify the vertices of the feasible region (possible
minimum and maximum solutions)
• Substitute each vertex into the objective function to
find the minimum or maximum
Varying types of problems
• Given the constraints and the objective
function
• Just a story/situation
Example 1
Example 2
Yum’s Bakery bakes two breads, A and B. One
batch of A uses 5 pounds of oats and 3
pounds of flour. One batch of B uses 2
pounds of oats and 3 pounds of flour. The
company has 180 pounds of oats and 135
pounds of flour available.
Write the constraints for the problem and
graph the feasible region. Set it up first…
• Identify variables
• Write a system
• Graph
Yum’s Bakery wants to maximize its profits
from bread sales. One batch of A yields a
profit of $40. One batch of B yields a profit of
$30. Use the profit information and the data
from Example 1 to find how many batches of
each bread the bakery should bake.
• Write Objective Function
• Identify Vertices
• Substitute into objective function