SEC 5 CST
September 2015
INTRODUCTION TO OPTIMIZATION
1. Given the polygon of constraints, determine the coordinates of the vertices.
Remember to label your vertices and place your information in a table of values!
a)
b)
SEC 5 CST
September 2015
c)
d)
SEC 5 CST
September 2015
2. Given the optimizing function, determine which of the vertices of the polygon of
constraints will maximize the solution.
a)
COORDINATES OF VERTEX
Z= 15x + 25y
A (80,20)
B (160,40)
C (180,20)
b)
COORDINATES OF VERTEX
A (100,104)
B (106,108)
C (110,106)
D (112,100)
Z= 16x + 32y
SEC 5 CST
September 2015
3. Given the optimizing function, determine which of the vertices of the polygon of
constraints will minimize the solution.
a)
COORDINATES OF VERTEX
A (4,18)
Z= 2x- 4y
B (17,14)
C (10,2)
D (3,12)
b)
COORDINATES OF VERTEX
A (4,15)
B (19,19)
C (11,5)
D (0,5)
Z= -7x – 3y
SEC 5 CST
September 2015
4. For each of the following:
a) x > 1
y>3
y>x+2
y < -2x + 20
OBJECTIVE: minimize
Z=x+y
-
Graph the system of inequalities
Determine the coordinates of the vertices
Identify the vertex that will allow you to attain the
objective
SEC 5 CST
September 2015
b) y < 2x + 5
y > -x + 5
y > 4x – 10
OBJECTIVE: maximize
Z = -2x + 4y
SEC 5 CST
September 2015
5. The graduation committee at school organizes a bake sale to raise money for prom.
Let x represent the number of cookies and y be the number of cupcakes.
OPTIMIZING FUNCTION
Price of a cookie is $1.25
Price of a cupcake is $2.00
Z = 1.25x + 2.00y
CONSTRAINTS
The committee must sell:
-
a maximum of 320 items ---------- > x + y < 320
at least 120 cookies ----------------- > x > 120
at most 160 cupcakes -------------- > y < 160
at most 4 times as many cookies as muffins ---- > 4y < x
OBJECTIVE
How many cupcakes and cookies have to be sold to maximize profits?