Question

The revenue equation​ (in hundreds of millions of​ dollars) for barley production in a certain country is approximated by R(x)=0.0628x^2+1.435x+2.1958 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 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 450,000,000 bushels. The marginal revenue is ................. hundred million dollars. (Type an integer or decimal rounded to two decimal places as​ needed.)

Answer 1

Solution:

A) The marginal revenue equation is obtained by differentiating the total revenue equation.

We have, total revenue equation is ,

R(x) = 0.0628x² + 1.435x + 2.1958

Hence, marginal revenue equation will be as follows:

The marginal revenue equation is R'(x) = 0.1256x + 1.435

B) We have to find marginal revenue for the production of 200,000,000 bushels.

In our marginal revenue equation x is in hundred million dollars.

200,000,000 = 2 hundred million dollars

Putting x = 2 in marginal revenue equation we get,

R'(x) = (0.1256 × 2) + 1.435

R'(x) = 1.6862

R'(x) = 1.69 (rounded to 2 decimal places)

The marginal revenue is 1.69 hundred million dollars.

C) We have to find marginal revenue for the production of 450,000,000 bushels.

In our marginal revenue equation, x is in hundred million dollars.

450,000,000 = 4.5 hundred million dollars

Putting x = 4.5 in marginal revenue equation we get,

R'(x) = (0.1256 × 4.5) + 1.435

R'(x) = 2.0002

R'(x) = 2.00 (rounded to 2 decimal places)

The marginal revenue is 2.00 hundred million dollars.

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