Download 3-4 Linear Programming Definitions: Linear Programming: Objective

3-4 Linear Programming
Definitions:
Linear Programming:
Objective Function:
Constraints:
Feasible Region:
Vertex Principle of Linear Programming:
Step 1: Graph the constraints
Step 2: Identify the vertices of the feasible region
Step3: Test the coordinates of the vertices in the objective function
Example. You have 30 acres to grow strawberries and tomatoes. You want at least 10 acres of strawberries.
You want at least 5 acres of tomatoes. The profit for strawberries is $80 per acre and the profit for tomatoes is
$60 per acre. How many acres of each should you plant to maximize your profit? What is the maximum profit?
Using linear programming, find the values of x and y that maximize and find the maximum.
E1 x0
y0
y3
x y 5
P  5x  8 y
E 2. x  2
yx
y 8
F  15 x  25 y
Huntington is in charge of decorating the school gym for graduation. He will need to buy gold and blue rolls of
crepe paper. Blue crepe paper costs $5 per roll and gold crepe paper costs $3 per roll. He will need at least
12 rolls of crepe paper. He wants no more than 6 rolls of blue and no more than 7 rolls of gold. How many
rolls of each color should he buy to minimize the cost? What is the minimum cost? Use linear programming.