(a) A chemical manufacturer sells sulfuric acid in bulk at a price of $100 per unit. If the daily total production cost in dollars for x units is
C(x) = 100, 000 + 50x + 0.0025x^2
and if the daily production capacity is at most 7000 units, how many
units of sulfuric acid must be manufactured and sold daily to maximize
the profit?
(b) Would it benefit the manufacturer to expand the daily production capacity?