3-4 Linear Programming

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

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

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

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

shreya owns a car and a moped. She has at most 12 litres of petrol to be used between the car and the moped. The car's tank holds at most 10 litres and the moped's 3 litres. The mileage for the car is 20 km/l and for the moped is 100 km/l. What are the variables you need to define?

• x is petrol, y is mileage

• x is car, y is moped

• x is petrol, y is moped

• x is car, y is mileage

Niki owns a car and a moped. She has at most 12 litres of petrol to be used between the car and the moped. The car's tank holds at most 10 litres and the moped's 3 litres. The mileage for the car is 20 km/l and for the moped is 100 km/l.

What are the constraints?

• x≤10, y≤3, x+y≤12

• 0≤x≤10, 0≤y≤3, x+y≤12

• x≥0, y≥0, 10x+3y≤12

• x≤10, y≤3, 10x+3y≤12

What do you call the area where all the shading overlaps?

• the answer

• the feasible region

• the void

• the objective function

Tags

CCSS.HSA.REI.D.12

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

Which vertex maximizes the profit?

• (0,0)

• (6,2)

• (8,0)

• (0,6)

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.12

CCSS.HSA.REI.C.6

CCSS.HSA.REI.D.10

Write the system of inequalities

Danish works at a movie theater selling tickets. The theater has 300 seats and charges Rs300 for adults and ₹ 250 for children. The theater expects to make at least Rs75000 for each showing.

• x+y≤300
  300x+250y≥75000, $x,y\ge0$

• x+y<300
  300x+250y≥75000, $x,y\ge0$

• $x,y\ge0$ ,x+y≤300
  300x+250y≤75000

• x+y>75000
  300x+250y≤300 , $x,y\ge0$

It involves planning of activities to obtain the best or optimal solution to a problem using limited resources to attain the goal

• Operations research

• Maximization

• Minimization

• Linear programming

Set of all points that satisfy all of the problem's resource restrictions

• extreme points

• intercepts

• feasible region

• graphical solution

Tags

CCSS.HSA.REI.D.12

Write the system of inequalities
Venu Gopal is drawing caricatures at a fair for 8 hours (480 minutes). He can complete a small drawing in 15 minutes and charges Rs500 for the drawing. He can complete a larger drawing in 45 minutes and charges Rs1250 for the drawing. Eiko hopes to make at least Rs10000 at the fair. 

• 10x+15y≤480
  45x+25y≥250 , $x,y\ge0$  

•  $x,y\ge0$  2x+5y≤40
  15x+45y≤480,

• 2x+5y>40
  15x+45y<480 , $x,y\ge0$  

• 2x+5y≥40
  15x+45y≤480 , $x,y\ge0$