Marginal revenue question?

Question

A factory owner who employes m workers finds that they produce

q=2.2 m(2.2 m+16)^3/2

units of product per day.

The total revenue r in dollars is

r = 531 q/((303405+5 q)^1/2)

.

(a) From the fact that

revenue = (price per unit)·(number of units)

it follows that, when there are 15 workers, the price per unit is ???dollars.

(b) When there are 15 workers, the marginal revenue is ???dollars/(one unit of product).

(c) The marginal-revenue product is defined as the rate of change of revenue with respect to the number of employees. Therefore

marginal−revenue product = dr / (dm)

.

If q and r are given as above then, when m= 15, the marginal-revenue product is ???dollars/(one worker). This means that if employee number 16 is hired, revenue will increase by approximately ???dollars per day.

Answer 1

a)

m=15

q=11319

r=10017.3

p=10017.3/11319=0.885

b)

TR=531Q/((303405+5Q)^1/2)

MR=(TR)'

Q(15)=11319

MR(Q=11319)=-(1327.5Q / (303405+5Q)^1.5)+

+531/(303405+5Q)^0.5= 0.815435

c)

MRP(15~16)=TR(m=16)-TR(m=15)=

=11289.81-10017.32 =1272.498