2.7 Optimization with Linear Programming

2.7 Optimization with Linear Programming

Wednesday, October 28 / 2020

Multiple Choice

Sarah makes small purses (x) and big purses (y). She can make no more than 8 purses a week.
Which inequality represents the situation?

• x + y ≤ 8
• x + y ≤ 6
• 2x + 3y ≤ 6
• x + y ≤ 10

Multiple Choice

Graph the system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum and minimum values of the function for this region.

3 ≤ y ≤ 6

y ≤ 3x + 12

y ≤ -2x + 6

f(x , y) = 4x - 2y

• A.) The maximum value is 0 at (0, 6). The minimum value is - 20 at (-3, 3).

• B.) The maximum value is 0 at (-3, 3). The minimum value is - 20 at (0, 6).

• C.) The maximum value is 0 at (-2, 6). The minimum value is - 20 at (1.5, 3).

• D.) The maximum value is 0 at (1.5, 3). The minimum value is - 20 at (-2, 6).

Multiple Choice

Maximize P = 3x + y with the following constraints:

 $x+y\ \le300$ 

 $y\ \ge100$  

 $x\ \le150$  

• A.) x = 0, y = 300

• B.) x = 150, y = 150

• C.) x = 100, y 150

• D.) x = 150, y = 100

Multiple Choice

Find the values of x and y that maximize the objective function P = 3x + 2y for the graph. What is the maximum value?

• A.) maximum value at (5, 4); 23

• B.) maximum value at (0, 8); 16

• C.) maximum value at (9, 0); 27

• D.) maximum value at (0, 0); 0

Multiple Choice

Given the objective function: P = 30x + 50y

Which vertex maximizes the profit?

• A.) (0,0)

• B.) (6,2)

• C.) (8,0)

• D.) (0,6)

Multiple Choice

In other words...what are the vertices of the feasible region?

• A.) (0, 0), (0, 6), (6, 2), (8, 0)

• B.) (0, 0), (6, 0), (2, 6), (0, 8)