Course: Mathematical Fundamentals Topic: Application of Derivatives in Economic Problems A manufacturer determines that "t" employees will produce a total of "q(t)" units per day, where: If demand equation for product (price) is given by: (a) Determine RATE OF CHANGE of income "I" with respect to "t" workers. b) What is RATE OF CHANGE of income when there are 12 workers?
Course: Mathematical Fundamentals
Topic: Application of Derivatives in Economic Problems
A manufacturer determines that "t" employees will produce a total of "q(t)" units per day, where:
<See attached image 1>
If demand equation for product (price) is given by:
<See attached image 2>
(a) Determine RATE OF CHANGE of income "I" with respect to "t" workers.
b) What is RATE OF CHANGE of income when there are 12 workers?
(a) The rate of change of income in derivative form can be written as
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Solved in 4 steps
First. Income function is Income = p(q) * q. I don't see that part in development.
Second. When there is variable "q" as (q+10)^2 on denominator , it can be replaced by q(t) from statement, since it asks for rate of change of I over t.
So I see that something is missing in development, to then replace t = 12 workers. And I think is "dI/dt", no "dp/dt", where dI is Income partial derivate
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