"he cost of producing x teddy bears per day at the Cuddly Companion Co. is calculated by their marketing staff to be given by the formula C(x) = 100 + 37x - 0.07x². a) Find the marginal cost function C'(x). C'(x) = || b) How fast is the cost going up at a production level of 100 teddy bears? When they produce 100 teddy bears, the production costs are increasing at a rate of [ n other words, the cost to produce the 101st |× dollars per teddy bear ]× dollars v teddy bear is approximately | c) Find the average cost function 7, and evaluate č(100). C(x) = C(100) = |x so when they produce 100 teddy bears, the average cost per teddy bear is x dollars.
"he cost of producing x teddy bears per day at the Cuddly Companion Co. is calculated by their marketing staff to be given by the formula C(x) = 100 + 37x - 0.07x². a) Find the marginal cost function C'(x). C'(x) = || b) How fast is the cost going up at a production level of 100 teddy bears? When they produce 100 teddy bears, the production costs are increasing at a rate of [ n other words, the cost to produce the 101st |× dollars per teddy bear ]× dollars v teddy bear is approximately | c) Find the average cost function 7, and evaluate č(100). C(x) = C(100) = |x so when they produce 100 teddy bears, the average cost per teddy bear is x dollars.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![The cost of producing \( x \) teddy bears per day at the Cuddly Companion Co. is calculated by their marketing staff to be given by the formula
\[ C(x) = 100 + 37x - 0.07x^2. \]
(a) Find the marginal cost function \( C'(x) \).
\[ C'(x) = \]
(b) How fast is the cost going up at a production level of 100 teddy bears?
When they produce 100 teddy bears, the production costs are increasing at a rate of
\[ \ \] dollars per teddy bear.
In other words, the cost to produce the 101st teddy bear is approximately
\[ \ \] dollars.
(c) Find the average cost function \( \overline{C} \), and evaluate \( \overline{C}(100) \).
\[ \overline{C}(x) = \]
\[ \overline{C}(100) = \]
So when they produce 100 teddy bears, the average cost per teddy bear is
\[ \ \] dollars.
(d) Fill in the blanks: Since the marginal cost is [less than/greater than] the average cost per unit, increasing production from 100 teddy bears will cause the average cost per unit to [increase/decrease].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9d9af5e6-9fd3-4a9b-a9c8-3b97e891ab83%2Fa83c58bb-7cc1-4f41-bc60-162aacb62d97%2F8vdfktt_processed.png&w=3840&q=75)
Transcribed Image Text:The cost of producing \( x \) teddy bears per day at the Cuddly Companion Co. is calculated by their marketing staff to be given by the formula
\[ C(x) = 100 + 37x - 0.07x^2. \]
(a) Find the marginal cost function \( C'(x) \).
\[ C'(x) = \]
(b) How fast is the cost going up at a production level of 100 teddy bears?
When they produce 100 teddy bears, the production costs are increasing at a rate of
\[ \ \] dollars per teddy bear.
In other words, the cost to produce the 101st teddy bear is approximately
\[ \ \] dollars.
(c) Find the average cost function \( \overline{C} \), and evaluate \( \overline{C}(100) \).
\[ \overline{C}(x) = \]
\[ \overline{C}(100) = \]
So when they produce 100 teddy bears, the average cost per teddy bear is
\[ \ \] dollars.
(d) Fill in the blanks: Since the marginal cost is [less than/greater than] the average cost per unit, increasing production from 100 teddy bears will cause the average cost per unit to [increase/decrease].
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