Question

The revenue equation​ (in hunderds of millions of​ dollars) for barley production in a certain country is approximated by

R(x)=0.0614 x squared +1.4394x+2.1237

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)=how. much

​(Round to four decimal places as​ needed.)

​(b) Find the marginal revenue for the production of 300,000,000 bushels.The marginal revenue is how much hundred million dollars.

(Type an integer or decimal rounded to two decimal places as​ needed.)

​(c) Find the marginal revenue for the production of 450,000,000 bushels.The marginal revenue is how much hundred million dollars.

​(Type an integer or decimal rounded to two decimal places as​ needed.)

Answer 1

a) The marginal revenue is computed by differentiating the revenue equation with respect to X, therefore we get here:

R'(x) = 0.0614*(2x) + 1.4394

R'(x) = 0.1228x + 1.4394

b) Here we are given that number of bushels as 300,000,000 that is 300 hundred millions, therefore X = 3 because x is in hundreds of millions of bushels

Therefore, we get here:

R'(x) = 0.1228*3 + 1.4394 = 1.8078

Therefore 1.81 is the required marginal revenue value here ( rounded to two decimal places )

c) Similar to the above part, here we are given that number of bushels as 450,000,000 that is 4.5 hundred million bushels, therefore X = 4.5 here.

R'(x) = 0.1228*4.5 + 1.4394 = 1.992

Therefore 1.99 is the required marginal revenue value here ( rounded to two decimal places )