Answer:
0 ≤ x < 1.12 and 34.18 < x ≤ 39.87
Step-by-step explanation:
Let
x ----> is the number of tires produced, in thousands
C(x) ---> the production cost, in thousands of dollars
we have
![C(x)=-0.34x^{2} +12x+62](https://tex.z-dn.net/?f=C%28x%29%3D-0.34x%5E%7B2%7D%20%2B12x%2B62)
This is a vertical parabola open downward (the leading coefficient is negative)
The vertex represent a maximum
The graph in the attached figure
we know that
Looking at the graph
For the interval [0,1.12) -----> ![0\leq x](https://tex.z-dn.net/?f=0%5Cleq%20x%3C1.12)
The value of C(x) ----> ![C(x) < 75](https://tex.z-dn.net/?f=C%28x%29%20%3C%2075)
That means ----> The production cost is under $75,000
For the interval (34.18,39.87] -----> ![34.18 < x\leq 39.87](https://tex.z-dn.net/?f=34.18%20%3C%20x%5Cleq%2039.87)
The value of C(x) ----> ![C(x) < 75](https://tex.z-dn.net/?f=C%28x%29%20%3C%2075)
That means ----> The production cost is under $75,000
Remember that the variable x (number of tires) cannot be a negative number
therefore
If the company wants to keep its production costs under $75,000 a reasonable domain for the constraint x is
0 ≤ x < 1.12 and 34.18 < x ≤ 39.87