(10 pts) (See textbook page 82 for definitions of the economie funetions used in

Question

(10 pts) (See textbook page 82 for definitions of the economie funetions used in this problem) The cost, in dollars, for a company to produce x widgets is given by ax)=5250+700r for x 2 0, and the price-demand function, in dollars per widget is p(x)-45-0.02x for O sx s 2250. a) Find and interpret Q300 b) Find and interpret C(300) (Note that Cix) is the average cost function) c) Find and simplify the expression for the revenue function Rix (work optional work optional) Note that pry and Find and simplify the expression for the profil finction Ptx Plx) are different functions. d) e) Find and interpret P300), where Ptx) is the peofit Put

Explanation / Answer

Ans(a):
C(x)=5250+7.00x
C(300)=5250+7.00*300=7350
So C(300) means cost for producing 300 widgets is $7350.

Ans(b):
C(x)=5250+7.00x
C'(x)=0+7.00*1=7
C'(300)=7
So C'(300) means cost per widget increases by $7.

Ans(c):
C(x)=5250+7.00x
p(x)=45-0.02x
Then revenue function R(x) is given by:
R(x)=C(x)*p(x)=(5250+7.00x)(45-0.02x)=236250-105x+315x-0.14x^2
R(x)=-0.14x^2+210x+236250

Ans(d):
C(x)=5250+7.00x
R(x)=-0.14x^2+210x+236250

profit function P(x) is given by
P(x)=R(x)-C(x)=(-0.14x^2+210x+236250)-(5250+7.00x)
P(x)=-0.14x^2+203x+231000

Ans(e):
P(x)=-0.14x^2+203x+231000
P(300)=-0.14(300)^2+203(300)+231000
P(300)=279300
that means profit on 300 widgets is $279300.

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