(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 + 50 x + 0.0025 x 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? (c) Use marginal analysis to approximate the effect on profit if daily production could be increased from 7000 to 7001 units.
(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 + 50 x + 0.0025 x 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? (c) Use marginal analysis to approximate the effect on profit if daily production could be increased from 7000 to 7001 units.
(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
+
50
x
+
0.0025
x
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?
(c) Use marginal analysis to approximate the effect on profit if daily production could be increased from
7000
to
7001
units.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Solve ANY Optimization Problem in 5 Steps w/ Examples. What are they and How do you solve them?; Author: Ace Tutors;https://www.youtube.com/watch?v=BfOSKc_sncg;License: Standard YouTube License, CC-BY
Types of solution in LPP|Basic|Multiple solution|Unbounded|Infeasible|GTU|Special case of LP problem; Author: Mechanical Engineering Management;https://www.youtube.com/watch?v=F-D2WICq8Sk;License: Standard YouTube License, CC-BY