The weekly demand for the Pulsar 25 color LED television is represented by p, wh

Question

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 = 500 - 0. 05x (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) = 0. 000009x3 - 0. 032x2 + 340x + 75000 Find the marginal revenue function. Find the marginal profit function. Find the marginal cost function.

Explanation / Answer

a)Total Revenue = p*x
= (500 - 0.05x)x
= 500x - 0.05x2

Marginal Revenue = Differentiation of Total Revenue w.r.t 'X'
     = d( 500x - 0.05x2) /dx
   = 500 - 0.1x (Ans)

b) Total Profit = Total Revenue - Total Cost
= (500x - 0.05x2) - (0.000009x3 - 0.032x2 +340x + 750000)
= 160x - 0.018x2 - 0.000009x3 - 750000

  Marginal Profit = Differentiation of Total Profit w.r.t 'X'
= d(160x - 0.018x2 - 0.000009x3 - 750000)/dx
= 160 - 0.036X - 0.000027x2 (Ans)

c) Marginal Cost = Differentiation of Total Cost w.r.t 'X'
= d(0.000009x3 - 0.032x2 +340x + 750000)/dx
= 0.000027x2 - 0.064x + 340 (Ans)

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