Question

Pulsar manufactures a series of 20-in. flat-tube LCD televisions. The quantity x of these sets demanded...

Pulsar manufactures a series of 20-in. flat-tube LCD televisions. The quantity x of these sets demanded each week is related to the wholesale unit price p by the equation

p = −0.059x + 290

The weekly total cost incurred by Pulsar for producing x sets is

C(x) = 0.000006x3 - 0.07x2 + 410x + 69000.

(a) Find the revenue function R.
R(x) =



Find the profit function P.
P(x) =

.011x2−120x−0.000006x3−69000

  

(b) Find the marginal cost function C '.
C '(x) =



Find the marginal revenue function R '.
R '(x) =



Find the marginal profit function P '.
P '(x) =



(c) Compute the following values. (Round your answers to two decimal places.)

C '(2400) =  
R '(2400) =  
P '(2400) =  

The quantity of Sensitech laser gaming mice demanded each month is related to the unit price by the equation

p =

60
0.01x2 + 1

      (0 ≤ x ≤ 20)

where p is measured in thousands of dollars and x in units of a thousand.

(a) Find the revenue function R.
R(x) =



(b) Find the marginal revenue function R'.
R'(x) =



(c) Compute R'(2). (Round your answer to three decimal places.)
R'(2) =

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