Math Problem Statement
A company manufacturing surfboard has fixed costs of $300 per day and total costs of $5,100 per day at a daily output of 20 boards. (A) Assuming that the total cost per day, C(x), is linearly related to the total output per day, x, write an equation for the cost function. (B) The average cost per board for an output of x boards is given by C̅(x)= C(x) /x. Find the average cost function. (C) Sketch a graph of the average cost function, including any asymptotes,
Solution
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Math Problem Analysis
Mathematical Concepts
Linear Functions
Average Cost Function
Asymptotes
Formulas
Cost function: C(x) = mx + b
Average cost function: C̅(x) = (240x + 300)/x = 240 + 300/x
Theorems
Linear Function Behavior
Asymptote Behavior in Rational Functions
Suitable Grade Level
Grades 10-12
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