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

The revenue equation​ (in hunderds of millions of​ dollars) for barley production in a certain country is approximated by Upper R left parenthesis x right parenthesisequals0.0688 x squared plus 1.2121 x plus 2.2234 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. ANSWERS NEEDED - Marginal revenue for 400,000,000 bushels for 550,000,000 bushels

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Answers:

Revenue equation:  R'(x) = 0.1376x + 1.2121

Marginal revenue for 400,000,000 bushels = 176.25 million dollars per hundred million bushels

Marginal revenue for 550,000,000 bushels = 196.89 million dollars per hundred million bushels

Explanations:

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

Upper R left parenthesis x right parenthesisequals0.0688 x squared plus 1.2121 x plus 2.2234

where x is in hundreds of millions of bushels.

In equation, we have

R (x) = 0.0688 x2 + 1.2121 x + 2.2234

Marginal revenue equation:

The Marginal revenue equation R'(x) is found by differentiating R(x) w.r.t x

Differentiating R(x), we get,

R'(x) = 0.0688*2x + 1.2121 + 0

Therefore,

R'(x) = 0.1376x + 1.2121

The marginal revenue for the production of the given number of bushels = 400,000,000 = 4 hundred millions

R'(4) = 0.1376 * 4 + 1.2121

= 1.7625 hundred million dollars per hundred million bushels

= 176.25 million dollars per hundred million bushels

= $176, 250, 000 dollars per hundred million bushels

The marginal revenue for the production of the given number of bushels = 550,000,000 = 5.5 hundred millions

R'(4) = 0.1376 * 5.5 + 1.2121

= 1.9689 hundred million dollars per hundred million bushels

= 196.89 million dollars per hundred million bushels

= $196, 890, 000 dollars per hundred million bushels

orchestra answered 1 year ago
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