Constraints and Objective Functions

It is a method for finding a maximum or minimum value of some quantity, given a set of constraints.

• Operations research

• Maximization

• Minimization

• Linear programming

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

• (0, 0), (0, 6), (6, 2), (8, 0)

• (0, 0), (6, 0), (2, 6), (0, 8)

When graphing constraints, what do you call the area where all the shading overlaps?

• the answer

• the feasible region

• the void

• the objective function

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

Which vertex maximizes the profit?

• (0,0)

• (6,2)

• (8,0)

• (0,6)

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

• maximum value at (5, 4); 32
• maximum value at (0, 8); 16
• maximum value at (9, 0); 27
• maximum value at (0, 0); 0

• (7,4)

• (3,10)

• (10,1)

• (8,5)

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 > 8

• 2x + 3y ≤ 6

• x + y ≤ 10

It takes Sarah 2 hours to make small purses and 3 hours to make big purses. She has a maximum of 18 hours a week. Which inequality represents this situation?

• 2x + 3y ≤ 18
• x + y ≤ 6
• x + y ≤ 9
• 3x + 2y ≤ 18

Sarah makes $30 for each small purse (x) and $50 for each big purse (y). What is the objective function?

• P = 30x + 50y

• P = 50x + 30y

Which of the following inequalities matches the given graph?

• y ≤ -3/4 x + 3
• y ≥ -3/4 x + 3
• y < -3/4 x + 3
• y > -3/4 x + 3