Answer:
The correct constraint is:
0 ≤ x ≤ 15
Explanation:
The function given to us in the question is:
y = -2x² + 30x + 200
It is given that the function is at least 200, we can write is as:
-2x² + 30x + 200 ≥ 200 ⇒ Equation (i)
To find the constraint, replace ≥ sign with = sign and solve for x:
-2x² + 30x + 200 = 200
-2x² + 30x = 0
x(-2x + 30) =0
x = 0 , -2x + 30 = 0
x = 0 , -2x = -30
x = 0 , x = -30/-2
x = 0 , x = 15
So the end values of constraint are 0 and 15.
Take any value between 0 and 15 and substitute in equation (i) to see whether it satisfies the equation or not.
-2x² + 30x + 200 ≥ 200
Substitute x = 5 in the equation:
-2(5)² + 30(5) +200 ≥ 200
-50 + 120 +200 ≥ 200
270 ≥ 200
As the equation satisfies. it means that the solution lies between 0 and 15, including the end values.
Hence.
0 ≤ x ≤ 15