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A company's revenue from selling units of an item is given as R = 1600x - 3x². If sales are increasing at the rate of 35 units per day, how rapidly is revenue increasing (in dollars per day) when 190 units have been sold? dollars per day

A company's revenue from selling units of an item is given as R = 1600x - 3x². If sales are increasing at the rate of 35 units per day, how rapidly is revenue increasing (in dollars per day) when 190 units have been sold? dollars per day

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A company's revenue from selling units of an item is given as R = 1600x − 3x². If sales are increasing at the rate of 35 units per day, how rapidly is revenue increasing (in dollars per day) when 190 units have been sold? dollars per day
Transcribed Image Text:A company's revenue from selling units of an item is given as R = 1600x − 3x². If sales are increasing at the rate of 35 units per day, how rapidly is revenue increasing (in dollars per day) when 190 units have been sold? dollars per day
Expert Solution
Step 1

Given, revenue in dollars of a company from selling x units of an item is

R(x) = 1600x - 3x2  -----------(i)

Also, given increasing rete of sale is 

dxdt = 35 units per day ;       where t is time in days

Also, given when 190 units have been sold then x = 190

That is, at dxdt = 35 and x = 190  

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