Answer:
The vertices feasible region are (0 , 15) , (10 , 15) , (20 , 5)
The minimum value of the objective function C is 125
Step-by-step explanation:
* Lets look to the graph to answer the question
- There are 3 inequalities
# y ≤ 15 represented by horizontal line (purple line) and cut the
y-axis at point (0 , 15)
# x + y ≤ 25 represented by a line (green line) and intersected the
x-axis at point (25 , 0) and the y- axis at point (0 , 25)
# x + 2y ≥ 30 represented by a line (blue line) and intersected the
x-axis at point (30 , 0) and the y-axis at point (0 , 15)
- The three lines intersect each other in three points
# The blue and purple lines intersected in point (0 , 15)
# The green and the purple lines intersected in point (10 , 15)
# The green and the blue lines intersected in point (20 , 5)
- The three lines bounded the feasible region
∴ The vertices feasible region are (0 , 15) , (10 , 15) , (20 , 5)
- To find the minimum value of the objective function C = 4x + 9y,
substitute the three vertices of the feasible region in C and chose
the least answer
∵ C = 4x + 9y
- Use point (0 , 15)
∴ C = 4(0) + 9(15) = 0 + 135 = 135
- Use point (10 , 15)
∴ C = 4(10) + 9(15) = 40 + 135 = 175
- Use point (20 , 5)
∴ C = 4(40) + 9(5) = 80 + 45 = 125
- From all answers the least value is 125
∴ The minimum value of the objective function C is 125
