Given that R(x)=200-x^2 and c(x)=5000+8x, for a new radio find each of the following P(x), R(175), C(175), and P(175)

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kjcdb8er's profile pic

kjcdb8er | Teacher | (Level 1) Associate Educator

Posted on

(P)rofit = (R)evenue - (C)ost

P(x) = R(x) - C(x) = 200 - x^2 - ( 5000 + 8x)

P(x) = 200 - 5000 - x^2 - 8x = -x^2 - 8x - 4800

R(175) = -30425

C(175) = 6400

P(175) = -36825

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

If you want this to be a model for revenue cost and profit model, there is a modification required to the model. The R(x) for the reciepts is 200-x^2 which implies the more the sales ( as quantity x of units sold increases0, then the revenue decreases which is harmful for the enterprise to self maintenance.The revenue going sqarely decreasing is not at all a healthy concept.

But since the models are given, the working method is simply as finding the functional value:

To find the functional value f(x) at x= a, substitute a for x in the function. Thus,

R(x) = 200 - x^2.

Therefore, R(175) =200-175^2 =-30425.

c(x) = 5000+8x.

Therefore, c(175) = 5000+8*175 = 6400.

The function P(x) is not defined. If P(x) = R(x)-c(x),

Then

P(x) = 200-x^2-(5000+8x) Or

P(175) = 200 - 175^2-(5000+8*175)

=200-30625-(5000+1400)

=-36825

 

 

 

 

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