1. Step 1: Define variables
x = number of "initial consultation" cases
y = number of "representing you" cases
p = total profit
Step 2: Make mixture table
initial consultations
representing you
constraints
paralegal time
1x
4y
20
lawyer time
1x
1y
8
Step 3: Write resource and situational constraints:
1 x 4 y ≤ 20
1 x 1 y ≤ 8
x≥ 0
y≥ 0
Step 4: Graph the system of inequalities, identify the vertices of the feasible region:
Vertices:
(0, 0)
(0, 5)
(8, 0)
(4, 4) from solving system of eq.
Step 5: Optimize according to your objective function, and make your recommendation:
p = 300 x  600 y
p = 300  0   600  0  = $0
p = 300  0   600  5  = $3000
p = 300  8   600  0  = $2400
p = 300  4   600  4  = $ 3600
Based on my analysis, the law firm should strive to accept 4 "initial consultations" and 4
cases of "representing you" to maximize profit at $3,600 each day.
Avery 2009
1. Step 1: Define variables
x = number of bikes
y = number of wagons
p = total profit
Step 2: Make mixture table
bikes
wagons
constraints
machine time
2x
3y
12
painting time
4x
2y
16
Step 3: Write resource and situational constraints:
2 x 3 y ≤ 12
4 x 2 y ≤ 16
x≥ 0
y≥ 0
Step 4: Graph the system of inequalities, identify the vertices of the feasible region:
Vertices:
(0, 0)
(0, 4)
(4, 0)
(3, 2) from solving system of eq.
Step 5: Optimize according to your objective function, and make your recommendation:
p = 12 x  10 y
p = 12  0   10  0  = $ 0
p = 12  0   10  4  = $ 40
p = 12  4   10  0  = $ 48
p = 12  3   10  2  = $56
Based on my analysis, the toy manufacturer should make 3 bikes and 2 wagons to
maximize profit at $56 each day.
Avery 2009
1. Step 1: Define variables
x = number of hot sites
y = number of cold sites
p = total profit
Step 2: Make mixture table
hot sites
cold sites
constraints
layout time
1.5x
1y
12
content time
1x
2y
16
Step 3: Write resource and situational constraints:
1.5 x1 y ≤ 12
1 x 2 y ≤ 16
x≥ 0
y≥ 0
Step 4: Graph the system of inequalities, identify the vertices of the feasible region:
Vertices:
(0, 0)
(0, 8)
(8, 0)
(4, 6) from solving system of eq.
Step 5: Optimize according to your objective function, and make your recommendation:
p = 50 x  250 y
p = 50  0   250  0  = $0
p = 50  0   250  8  = $ 2000
p = 50  8   250  0  = $ 200
p = 50  4   250  6  = $ 1700
Based on my analysis, Websites-R-US should strive to maintain 0 hot sites and 8 cold
sites to maximize profit at $2,000 each day.
Avery 2009