(a) Find the revenue function R . R ( x ) = 1 Find the profit function P . P ( x
ID: 2846467 • Letter: #
Question
(a) Find the revenue function R.R(x) = 1
Find the profit function P.
P(x) = 2
(b) Find the marginal cost function C '.
C '(x) = 3
Find the marginal revenue function R '.
R '(x) = 4
Find the marginal profit function P '.
P '(x) = 5
(c) Compute the following values. (Round your answers to two decimal places.)
C '(1100) = 6 R '(1100) = 7 P '(1100) = 8 1 2 3 4 5 C '(1100) = 6 R '(1100) = 7 P '(1100) = 8 The weekly demand for the Pulsar 25 color LED television is represented by p, where p denotes the wholesale unit price in dollars and x denotes the quantity demanded. p = 520 - 0.1x (0 x 12000) The weekly total cost function associated with manufacturing the Pulsar 25 is given by C(x), where C(x) denotes the total cost incurred in producing x sets. $ C(x) = {color{red}0.000004} x^3 - {color{red}0.09} x^2 + {color{red}350} x + {color{red}88000} $ Find the revenue function R. R(x) = Find the profit function P. P(x) = Find the marginal cost function C'. C'(x) = Find the marginal revenue function R '. R'(x) = Find the marginal profit function P'. P'(x) = Compute the following values. (Round your answers to two decimal places.)
Explanation / Answer
a) Revenue function = Price * Quantity = 520x - 0.1*x^2
Profit Function = Revenue - cost = (520x - 0.1*x^2 ) - ( 0.000004*x^3 - 0.09*x^2+350*x+88000 )
Profit function = - 0.000004*x^3 - 0.01*x^2+170*x - 88000
b) Marginal Cost function : 0.000012*x^2 - 0.18*x+350
Marginal revenue function : 520 - 0.2*x
Marginal Profit function = - 0.000012*x^2 - 0.02*x+170
c) C'(1100) = 1452-198+350 = 1604
R'(1100) = 520-220 = 300
p'(1100) = -1452-22+170 = -1304
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