The total cost (in dollars) of producing x college textbooks is C(x) = 50x+ 11,000
What is the fixed cost? 11,000
What is the marginal cost?
What is the total cost of producing 700 books? 34,000 books?
What is the average cost when 700 books are produced? When 34,000 books are produced?
(a) ok
(b) dC/dx = 50
(c) C(700), C(34000)
(d) C(n)/n
dC/dx=50
To find the marginal cost, we need to calculate the derivative of the cost function C(x) with respect to x.
C(x) = 50x + 11,000
Taking the derivative of this function, we get:
C'(x) = 50
So, the marginal cost is constant and equal to 50 dollars per textbook.
To find the total cost of producing 700 books, we substitute x = 700 into the cost function:
C(700) = 50(700) + 11,000
= 35,000 + 11,000
= 46,000 dollars
To find the total cost of producing 34,000 books, we substitute x = 34,000 into the cost function:
C(34,000) = 50(34,000) + 11,000
= 1,700,000 + 11,000
= 1,711,000 dollars
The average cost when producing 700 books can be calculated by dividing the total cost by the quantity:
Average cost for 700 books = C(700)/700
= 46,000/700
= 65.71 dollars
The average cost when producing 34,000 books can be calculated by dividing the total cost by the quantity:
Average cost for 34,000 books = C(34,000)/34,000
= 1,711,000/34,000
= 50.32 dollars
To find the marginal cost, we need to calculate the derivative of the total cost function with respect to the number of books produced.
C(x) = 50x + 11,000
The derivative of C(x) with respect to x is the marginal cost (MC):
MC = dC(x)/dx = 50
The marginal cost is a constant value of 50 dollars.
To find the total cost of producing a specific number of books, we substitute the value of x into the total cost function C(x):
For 700 books:
C(700) = 50 * 700 + 11,000
C(700) = 35,000 + 11,000
C(700) = 46,000
The total cost of producing 700 books is $46,000.
For 34,000 books:
C(34,000) = 50 * 34,000 + 11,000
C(34,000) = 1,700,000 + 11,000
C(34,000) = 1,711,000
The total cost of producing 34,000 books is $1,711,000.
To find the average cost when a certain number of books are produced, we divide the total cost by the number of books:
For 700 books:
Average Cost = C(700)/700
Average Cost = 46,000/700
Average Cost ≈ $65.71
The average cost when 700 books are produced is approximately $65.71.
For 34,000 books:
Average Cost = C(34,000)/34,000
Average Cost = 1,711,000/34,000
Average Cost = $50
The average cost when 34,000 books are produced is $50.