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