he revenue equation (in hunderds of millions of dollars) for barley production i
ID: 2780913 • Letter: H
Question
he revenue equation (in hunderds of millions of dollars) for barley production in a certain country is approximated by R(x)= 0.0619x^2+1.2921x+2.1915 where x is in hundreds of millions of bushels. Find the marginal-revenue equation and use it to find the marginal revenue for the production of the given number of bushels.
a) The marginal-revenue equation is R(x)= ?.
b) Find the marginal revenue for the production of 100,000,000 bushels.
The marginal revenue is _____ in hundred million dollars.
c) Find the marginal revenue for the production of 550,000,000 bushels.
The marginal revenue is _____ in hundred million dollars.
Explanation / Answer
R(x)= 0.0619x^2+1.2921x+2.1915
a) The marginal revenue measures the change in the revenue that arises when one additional unit of a product is sold. The marginal revenue is calculated by dividing the change in the total revenue by the change in the quantity. In calculus terms, the marginal revenue is the first derivative of the total revenue function with respect to the quantity: MR = dTR/dQ.
R(x)=d(R(x)/dx
= d(0.0619x^2+1.2921x+2.1915)/dx
=0.1238x+1.2921
b) Putting x= 1 hundreds of millions bushels in the equation(a)
R(x)= 0.1238(1)+1.2921
= 1.4159
The marginal revenue is 1.4159 in hundred million dollars.
c) Putting x= 5.50 hundreds of millions of bushels
R(x) = 0.1238(5.50) + 1.2921
= 1.9730
The marginal revenue is 1.9730 in hundred million dollars.
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