3.3 Optimization

3.3 Optimization

Multiple Choice

Solve the system of inequalities by graphing.

x ≤ 2

y > 3

Multiple Choice

Solve the system of inequalities by graphing.

y ≤ 3x + 2

y > –x

Multiple Choice

Graph the following system of inequalities. What are the maximum and minimum values of the function f(x, y) = 4x – 3y for the feasible region of the graph?

x ≤ 4 y ≤ 5 x + y ≥ 6

• maximum: f(4, 5) = 5

  minimum: f(1, 5) = –11

• maximum: f(4, 2) = 10

  minimum: f(1, 5) = –11

• maximum: f(4, 2) = 10

  minimum: f(4, 5) = 5

• maximum: f(1, 5) = –11

  minimum: f(4, 2) = 10

Multiple Choice

Graph the following system of inequalities. What are the maximum and minimum values of the function f(x, y) = x + 2y for the feasible region of the graph?

x + 3y ≤ 6

–x – 3y ≤ 9

2y – x ≥ –6

• maximum: no maximum

  minimum: f(6, 0) = 6

• maximum: f(6, 0) = 6

  minimum: f(0, –3) = –6

• maximum: f(6, 0) = 6

  minimum: no minimum

• maximum: no maximum

  minimum: f(0, –3) = –6

Multiple Choice

What is a combination of raking leaves and mulching that will maximize the income the company receives per day from one of its crews?

• 0 mulching; 2 raking

• 4 mulching; 0 raking

• 0 mulching; 4 raking

• 2 mulching; 0 raking