Mrs. Conway, Algebra II Honors
Freeman High School
Name: ____________________________
Monday, January 17, 2012
Practice 1: Maximum for P = 3x + 2
𝑥≤5
{𝑦 ≤ 4
𝑥 ≥ 0, 𝑦 ≥ 0
Practice 2: Minimum for P = -3x - 12y
𝑥+𝑦 ≥8
{𝑦 ≥ 5
𝑥≥0
y
y
–8
–6
–4
8
8
6
6
4
4
2
2
–2
–2
2
4
6
8
–8
x
–6
–4
–2
–2
–4
–4
–6
–6
–8
–8
Practice 3.: Maximum for P = 3x - 2y
𝑥+𝑦 ≥8
{1 ≤ 𝑦 ≤ 5
2≤𝑥≤6
2
–6
–4
8
x
y
8
8
6
6
4
4
2
2
–2
–2
6
Practice 4: Maximum for P=2x+y
3𝑥 + 𝑦 ≤ 7
{ 𝑥 + 2𝑦 ≤ 9
𝑥 ≥ 0, 𝑦 ≥ 0
y
–8
4
2
4
6
8
x
–8
–6
–4
–2
–2
–4
–4
–6
–6
–8
–8
2
4
6
8
x
Practice 5: Maximum for C = 10,000x + 20,0000y Practice 6: Minimize for P = 3x – 2y
3
5𝑥 + 𝑦 ≥ 10
𝑦
≥
𝑥−3
𝑥+𝑦 ≥6
2
{
{
𝑦 ≤ −𝑥 + 7
𝑥 + 4𝑦 ≥ 12
𝑥 ≥ 0, 𝑦 ≥ 0
𝑥 ≥ 0, 𝑦 ≥ 0
y
y
–12 –10 –8
–6
–4
12
12
10
10
8
8
6
6
4
4
2
2
–2
–2
–4
–6
–8
–10
–12
2
4
6
8
10
12
x
–12 –10 –8
–6
–4
–2
–2
–4
–6
–8
–10
–12
2
4
6
8
10
12
x