Answer to Question #100423 in Calculus for Lucas

Question

suppose that a company manufactures flash drives has a revenue of given by: R(x)10x-.001x^2
where the production output in 1 week is x flash drives. If production is increasing at a rate of 650 flash drives per week when production is 6000 flash drives find the rate of increase in revenue.

Answer 1

In this we have to find out the rate of increase in revenue which will be calculated by finding out the derivative of the R(x)

so we have been given R(x)=10x-0.001x²

where the production output in 1 week is x flash drives

now, differentiating R(x) with respect to t

we get , R'(x)=10*x'-0.001*2*x*x' ......(1)

where x' is the the derivative of x with respect of t which is basically the rate of increase of production per week

given in the question x= 6000 and x'= 650

on substituting the values of x and x' in equation (1)

we get R'(x)=10*650-0.001*2*6000*650

R'(x)=6500-12*650

R'(x)=-1300

hence the value of R'(x) comes out to be negative which means rate of revenue will decrease

rate of increase in revenue = -1300