Linear Programming Problems

Linear Programming

Objectives

• Use linear programming to find the great and least values to an expression in a region

• Apply linear programming in daily problems

Translating Problems into Mathematical expressions

• The number of students maximum 20: S⩽20

• The number of cars is not less than 100: C⩾100

• Keywords: Maximum, minimum, less than, greater than

Multiple Choice

Which of the following expressions shows the sentence: The number of score (A) maximum is 90.

• A>90

• A<90

• $$A\ge0$$

• $$A\le90$$

Multiple Choice

Which of the following shows the sentence:

The number of cars (C) and motorcycles (M) is not less than 120?

• M+C>120

• M+C<120

• $$M+C\le120$$

• $$M+C\ge120$$

Example 2: Finding the greatest and least values

Question:

Find the greatest and least values for the profit equation: P= 2x+5y

1. Find the three points of intersection.

2. Check the values of P= 2x+5y using the three corners

   1. Which ordered pair gives us the greatest value?

   2. Which ordered pair gives us the least value?

Multiple Choice

Which coordinate is located in the 3rd quadrant?

• (0,4)

• (4,0)

• (-4,-2)

• (-2,2)

Multiple Choice

Which coordinate is located in the 2nd quadrant?

• (0,4)

• (4,0)

• (-4,-2)

• (-2,2)

Multiple Choice

Which coordinate is located on the x-axis?

• (0,4)

• (4,0)

• (-4,-2)

• (-2,2)

Finding the greatest and least values

• Find the greatest and least values of 2x+y

• Check the values of 2x+y using the three corners (4,0), (-2,2) and (-4,-2)

• For (4,0) --> 2x+y --> 2.4+0=8