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3 years ago

How do you solve radical and division to this problem

Mathematics

1 answer:

Nadusha1986 [10]3 years ago

4 0

15/4 = 3.75;
$\sqrt{15/4} = \sqrt{15} /2 = 3.87/2 = 1.935;$

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Answer:

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b. $\frac{dR(q)}{dq}=-0.01q+200$

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Step-by-step explanation:

a) The marginal cost function is given by the derivative of the total cost function, in this way the marginal cost function for this company is:

$\frac{dC(q)}{dq} = \frac{dC(q)}{dq} (0.000004q^ 3 - 0.03q ^ 2 + 100q + 75000) = 0.000012q^2 -0.06q + 100$

b) The income function is given by the relation $R (q) = P (q) q = -0.005q^2 + 200q$ .

The marginal revenue function for the company is given by the derivative of the revenue function, in this way the marginal revenue function is:

$\frac{dR(q)}{dq}= -0.01q+200$

(c) The profit function of the company is given by the relation $U (q) = R (q) - C (q)$ , and the marginal utility function is given by the derivative of the utility function, in this way , the marginal utility function is:

$\dfrac{dU(q)}{dq}=R'(q) - C'(q) = -0.01q+200 - (0.000012q^2-0.06q+100) = -0.000012q^2+0.05q+100$

When q = 2000, the marginal utility is:

$U'(2000)=-0.000012(2000)^2+0.05(2000)+100 = 152$

When q = 7000, the marginal utility is:

$U'(7000)=-0.000012(7000)^2+0.05(7000)+100 = -138$

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