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The price-demand equation and the cost function for the production of table saws are...
The price-demand equation and the cost function for the production of table saws are given, respectively, by
x = 8400 – 36p and C(x) = 60000 + 72x, where x is the number of saws that can be sold a price of $p per saw and C(x) is the total cost (in dollars) of producing a saw. (A) Express the price p as a function of the demand x. (B) Find the marginal cost. (C) Find the revenue function, marginal revenue, profit function, and marginal profit.
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Number of saws = x = 8400 - 36p
Total cost of production = C(x) = 60000 + 72x
Where p = price per saw.
(A) Price p as function of demand x
We get this by rearranging the terms in equation for x as follows:
x = 8400 - 36p
36p = 8400 - x
Therefore price as a function of x is represented by
P(x) = 8400/36 - x/36 = 300 - x/36
(B) Marginal cost
Marginal cost is represented by the slope of the cost curve C(x) = 60000 + 72x
This is equal to 72.
Therefor marginal cost is $72
(C) - 1. Revenue Function
Revenue is given by the function
R (x)= Price function * Volume = P(x)*x
= (300 - x/36)*x = 300x - x^2/36
(C) - 2. Marginal Revenue
Marginal revenue is represented by the slope of the revenue curve, R(x) = 300x - x^2/36
This slope is represented by Derivative of R(x)
Marginal Revenue Function = M(x) = R'(x) = 300 - x/18
(C) - 3. Profit function
Profit function = S(x) = Revenue function - Cost Function = R(x) - C(x)
= (300x - x^2/36) - (60000 + 72x)
= - x^2/36 + 228x - 60000
(C) - 4. Marginal Profit
Marginal profit is represented by the slope of the profit curve, S(x) = x^2/36 + 228x - 60000
Marginal Profit function = S'(x) = - x/18 + 228
Posted by krishna-agrawala on March 29, 2010 at 12:01 AM (Answer #1)
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