Answer:
[tex]\bar C = 4100\,dollars[/tex]
Step-by-step explanation:
a) The average value of a function is given by the following integral:
[tex]\bar C = \frac{\int\limits^{q_{max}}_{0} {4100+90\cdot q^{2}} \, dq }{q_{max}}[/tex]
[tex]\bar C = \frac{1}{q_{max}}\cdot \left(4100\cdot q_{max} + 30\cdot q_{max}^{3} \right)[/tex]
[tex]\bar C = 4100 + 30\cdot q_{max}^{2}[/tex]
b) The determination of the minimum average daily cost per pound of pollutant is done by the First Derivative Test and the Second Derivative Test, which is:
[tex]\bar C' = 60\cdot q_{max}[/tex]
[tex]60\cdot q_{max} = 0[/tex]
[tex]q_{max} = 0[/tex]
[tex]\bar C'' = 60[/tex] (absolute minimum).
The level of reduction corresponding to the lowest average daily cost per pound of pollutant is:
[tex]\bar C = 4100\,dollars[/tex]
