Linear Programming Test 1

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

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

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

• x + y ≤ 8
• x + y ≤ 6
• 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

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

Is (-2,4) a solution to the system?

• Solution
• Not a solution

Match the system to the graph (solution set is on the left)

• y ≤ 3x   and  y ≤ -2x + 4
• y > 3x   and  y > -2x + 4
• y < 3x   and  y > -2x + 3
• y > 3x   and  y < -2x + 4