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Sagot :
Answer:
[tex]P = 20 - 2Q[/tex]
Explanation:
[tex]Q = 10 - 0.5P[/tex]
Price function can be estimated by inverting the demand function.
[tex]Q = 10 - 0.5P \\\\0.5P = 10 - Q\\P = 10/0.5 - Q/0.5 \\P = 20 - 2Q[/tex]
This is the price function.
Total revenue function can be estimated using the given formula,
[tex]TR = P*Q \\ = (20 - 2Q) Q \\ = 20Q - 2Q^2[/tex]
The linear demand function is given by,
[tex]Q = 400 - 250P \\[/tex]
Price function is given by,
[tex]P = 1.6 - 0.004Q \\[/tex]
Total revenue function is thus given by,
[tex]TR = P*Q \\ = 1.6Q - 0.004Q^2[/tex]
[tex]Y = 5(2X+3)^2 - 2X^2 \\Y = 5(4X^2 + 9 + 12X) - 2X^2\\Y = 20X^2 + 45 + 60X - 2X^2\\Y = 18X^2 + 45 + 60X \\[/tex]
The derivative of Y with respect to x is,
[tex]dY/dX = 36X + 60\\[/tex]
Equating this equal to 0 we get,
[tex]36X + 60 = 0 \\36X = -60 \\X = -10/6 \\\\X= -1.66[/tex]
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