Having Trouble with the below questions

Question

I'm having trouble answering the two below questions.

 

1.  The cost, in dollars, to produce x number of equipment is C(x) = 100x + 2000, x > 0 and the price-demand function, in dollars per equipment is p(x) = 550 - 10x, where 55 > x > 0. C(x) denotes the cost to produce x items and p(x) denotes the price-demand function in the given economic scenario.

 

a)  Find and interpret C(0)

 

b)  Find and interpret C(10)

 

c)  Find and interpret p(10)

 

d)  Find R(x)

 

e)  Find and simplify P(x)

 

f)  Solve P(x) = 0 and interpret

 

2.  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) = 150x + 2500, x > 0 and the price-demand function, in dollars per basket is p(x) = 450 dollars, where 90 > x > 0.

 

a) Find and interpret C(0)

b) Find and interpret C(10)

c) Find and interpret p(10)

d) Find R(x)

e) Find and simplify P(x)

f) Solve P(x) = 0 and interpret

Answer 1

1a)  Just plug in x=0 and compute C(x=0).   This is your cost when no units (x=0) are sold.

 

       C(x) = 100x + 2000

      C(x=0)= 100*0 + 2000 = 2000

 

1b)  Plug x=10 into the cost equation.  This is the cost when 10 units (x=10) are sold.

 

       C(10) = 100*10 + 2000 = _______

 

1c)  Plug x=10 into the price equation, p(x).  This is the unit price when 10 units (x=10) are sold.

 

       p(10) = 550 - 10*10 = _______

 

1d) Revenue, R(x), is the unit price (p(x)) times the number of units sold (x):

 

      R(x) = p(x)*x = (550 - 10x)*x = 550x - 10x²

 

Problem 2 works just like problem 1.  Try it on your own.