Answer:
200
Step-by-step explanation:
C = 0.007x² − 2.8x + 100
There are two ways we can find the minimum. The first is by noticing that this is an upwards parabola, so the minimum is at the vertex. For y = ax² + bx + c, the vertex is at x = -b/(2a).
x = -(-2.8) / (2 × 0.007)
x = 200
Alternatively, we can minimize C using calculus. Take the derivative with respect to x and set to 0:
dC/dt = 0.014x − 2.8
0 = 0.014x − 2.8
x = 200
