Practice 3 - Problem Formulation

A special case when an Linear Programming problem has no solution even though all constraints are being satisfied.

• alternate solutions

• infeasibility

• unboundedness

• redundancy

A special case in Linear Programming wherein there is a constraint that does not affect the feasible region.

• alternate solution

• infeasibility

• unboundedness

• redundancy

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 , $x,y\ge0$

Solve the  system by substitution. 

y = −6x + 3
−18x − 3y = 4 

• (−3, 8) 
• (−8, −3) 
• (2, −3) 
• No Solution

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Solve by elimination.
3x + y = -8
-2x - y = 6

• (-2, -2)
• (2, 2)
• (2, -14)
• (2, -10)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

[Multiple Answers] Which of these coordinate points lies within the feasible region?

• (5,3)

• (6,5)

• (5,1)

• (1,2)

• 2700

• 2650

• 2450

• 2300

A farmer has asked you for advice on the best strategy for planting wheat and corn on her 500-acre farm. To make it through harvest time, each acre of wheat she plants will require 1 person-day of labor and other expenses of $20. Each acre of corn she plants will require 5 person-days of labor and expenses of $30. The farmer has $11,400 and 1480 person-days of labor available, and she expects to make a profit of $90 per acre of wheat and $120 per acre of corn. If x = acres of wheat and y = acres of corn, which of the following is NOT a constraint?

• x + y ≤ 500
• 20x + 30y ≤ 11,400
• y ≥ 5x + 30
• x + 5y ≤ 1480

A chemist started an experiment with 5 grams of a chemical. The chemical is used at a rate of 0.01 grams per minute. Which of the following equations best describes the relationship between t, the time in minutes, and c, the amount of chemical remaining?

• c=0.01t-5
• c=5-0.01t
• c=5.01t
• c=4.99t

Tags

CCSS.HSF-BF.A.1A

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?

• 1.5x+0.5y=78.5
  x+y=87
• 1.5x+0.5y=78.5
  1.5x+0.5y=87
• x+y=78.5
  1.5x+0.5y=87
• x+y=78.5
  x+y=87

Tags

CCSS.HSA.CED.A.3