The revenue equation (in hunderds of millions of dollars) for barley production

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.)

Explanation / Answer

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 )

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