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Sagot :
The demand function for the marginal revenue function is found as; p(x) = 0.02x² - 0.025x + 138.
Explain the term revenue function?
- The relationship between the demand function p(x) as well as the revenue function R(x) is given by the equation R(x)=xp(x), where x represents the quantity of units sold.
- In order to get the revenue function, we shall integrate the marginal revenue function R′(x).
For the given question;
R′(x) = 0.06x² − 0.05x + 138
R(x) = ∫R′(x)dx
R(x) = ∫[0.06x² − 0.05x + 138] dx
R(x) = 0.06x³/3 - 0.05x²/2 + 138x + C
R(x) = 0.02x³ - 0.025x² + 138x + C
If R(0) = 0, revenue is 0.
Put x = 0.
0.02x³ - 0.025x² + 138x + C = 0
c = 0
Thus,
R(x) = 0.02x³ - 0.025x² + 138x
Factorizing the function,
R(x) = 0.02x³ - 0.025x² + 138x
R(x) = x(0.02x² - 0.025x + 138)
R(x) = xp(x) . Thus,
p(x) = 0.02x² - 0.025x + 138
Therefore, the demand function for the marginal revenue function is found as; p(x) = 0.02x² - 0.025x + 138.
To know more about the revenue function, here
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