Question

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

R(x)=0.0632x² + 1.2443x + 2.2473 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)= -------------------------. ​(Round to four decimal places as​ needed.)

​(b) Find the marginal revenue for the production of 200,000,000 bushels.The marginal revenue is----------------

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

​(c) Find the marginal revenue for the production of 550,000,000 bushels.The marginal revenue is----------------------- hundred million dollars. ​(Type an integer or decimal rounded to two decimal places as​ needed.)

Answer 1

(a)

R(x)=0.0632x² + 1.2443x + 2.2473

The​ marginal-revenue equation is R′(x)= 0.0632 * 2 x + 1.2443

R′(x)= 0.1264 x + 1.2443

(b)

For 200,000,000 bushels, x = 200,000,000 / (100 * 1,000,000) = 2

The marginal revenue is  0.1264 * 2 + 1.2443 = 1.4971 1.50

(c)

For 550,000,000 bushels, x = 550,000,000 / (100 * 1,000,000) = 5.5

The marginal revenue is  0.1264 * 5.5 + 1.2443 = 1.9395 1.94