3. 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 + 0.0025a2 %3D and if the daily production capacity is at most 7000 units. (a) 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 capac- ity?

Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.CR: Review Problem Set
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3. 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 + 0.0025x2
and if the daily production capacity is at most 7000 units.
(a) 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 capac-
ity?
Transcribed Image Text:3. 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 + 0.0025x2 and if the daily production capacity is at most 7000 units. (a) 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 capac- ity?
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