Linear Programming

Which are vertices of the feasible region?

• (0, 3) (3, 0) (5, 8)

• (0, 6) (3, 5) (6, 5)

• (3, 3) (8, 5) (5, 8)

• (0, 5) (6, 0) (3, 3)

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)

Which graph represents the system of inequalities shown to the left, indicated by the darkest blue shading?

• 
• 
• 
• 

The graph of 
y ≥  x - 3 
uses a __?__ line

• Dashed
• Solid
• Horizontal
• Vertical

Objective quantity:
P = 30x + 50y
Corner that maximizes profit: (0, 6)
What is the profit?

• 300
• 280
• 400
• 240

Write the system of inequalities
Carlos works at a movie theater selling tickets. The theater has 300 seats and charges $7.50 for adults and $5.50 for children. The theater expects to make at least $2000 for each showing.  

• x+y≤300
  7.5x+5.5y≥2000
• x+y<300
  7.5x+5.5y≥2000
• x+y≤300
  7.5x+5.5y≤2000
• x+y>2000
  7.5x+5.5y≤300

The graph of 
y ≥  x - 3 
is shaded ???

• Over / Above
• Under / Below

Define feasible region.

• A collection of all possible solutions. On the graph, it is where the shading overlaps.

• Limits put on possible outcomes.

• Money you make, after expenses.

• Vertices where the lines intersect.

_________ are the restrictions or limitation imposed on the linear programming problem.

• Cost

• Variables

• Constraints

• Profit