Find and Interpret

Question

Baskets, Inc., is planning to introduce a new woven basket. The company estimates that the cost (in dollars) to manufacture x baskets will be C(x) = 26x + 500, x ≥ 0 and
the price-demand function, in dollars per basket is p(x) = 32 dollars, 0 ≤ x

Please answer the following:
a) Find and interpret C(0).
b) Find and interpret C(10).
c) Find and interpret p(5)
d) Find R(x).
e) Find and simplify P(x).

Answer 1

If cost equation is given as a function of x -> C(x) it follows that:

 

a) C(0) is the cost when x=0    -> C(0)=26*0+500-500

 

b)Similarly, C(10) is the cost when x=10   -> C(10)=26*10+500=760

 

c)p(5) is the price equation when x=5   -> p(x)=32 for x greater than or equal to 0, thus, p(5)=32

 

d)Assuming R(x) is revenue equation which is given by quantity*price, thus, R(x)=x*p(x)=32x

 

e)Assuming P(x) is the profit equation which is given by P(x)=R(x)-C(x), we can say that P(x)=32x-26x-500=6x-500