Total revenue is in dollars and x is the number of units. Suppose that the total

Question

Total revenue is in dollars and x is the number of units.

Suppose that the total revenue function for a commodity is R = 35x 0.01x2.

a) find R(100)      Answer:$ 3400

b) Find the marginal revenue function     Answer:__MR=

c) find the marginal revenue at x=100         Answer:_________________

D)    Tell what it predicts about the sale of the next unit and the next 3 units.
                The sale of the next unit will increase the revenue by about $_____________. The sale of the next 3 units will increase the revenue by about $______________

E) Find R(101)-R(100)      Answer:________

Explanation / Answer

given revenue R = 35x 0.01x2

a)R(100) =35*100 0.01*1002

R(100) =3400

b)differentiate with respect to x

MR=dR/dx =35*1 -0.01*2x2-1

marginal revenue function =35 -0.02x

c)marginal revenue at x=100 is =35 -0.02*100

marginal revenue at x=100 is =35 -2

marginal revenue at x=100 is =33

D)sale of next unit increases revenue by 33 dollar

sale of next 3units increases revenue by 3*33 =99 dollar

E)R(101)-R(100)

=(35*101 0.01*1012)-(35*100 0.01*1002)

=32.99 dollars

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