Calculus

gillgill

1. Assume that total revenue from the sale of x television sets is given by
R(x)=1000(1-(x/5))^2
a)find the marginal revenue when 400, 500, 600 sets are sold
i found that R'(x)=-4 +(x/125)
is it correct?
therefore R'(400)=$-0.8 R'(500)=$0 R'(600)=$0.8
??

b)find the average revenue form the sales of x sets
ave R(x)=R(x)/x
would it equal (1000/x)(1-(x/500))^2 ??
could it be simplify further?

c) Find the marginal average revenue.
ave R'(x)=R'(x)/x
=(-4/x)+(1/125)

am i correct on all of these??

2. The cost is dollars of manufacturing x items is given by
C=2000x+3500
demand equation is x=√(15000-1.5p)
in terms of the demand x,
a) find an expression for the revenue R

does that mean R(x)=px
R(x)=p√(15000-1.5p)
or u solve for p instead?

homology

Nope, applying the chain rule you get (-1/5)*(2)*1000(1-(x/5)) which, upon simplification yields R'(x)=-400+80x
Kevin

gillgill

o..my mistake...the question is actually
R(x)=1000(1-(x/500))^2
then is my answer right now?

homology

yep, at least as far as R'(x) is concerned, I don't know any economics so I won't say anything else about the rest of the problem.