MHB Cost Functions for a Firm: Marginal & Average Cost

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The cost function for a firm is defined as C(x) = 300x - 10x^2 - 1/3x^3. The marginal cost function can be derived by taking the first derivative of the cost function, resulting in MC(x) = 300 - 20x - x^2. The average cost function is obtained by dividing the total cost by the output, yielding AC(x) = (300x - 10x^2 - 1/3x^3) / x. To find the output level where marginal cost equals average cost, set MC(x) equal to AC(x) and solve for x. This analysis is crucial for understanding cost management in production.
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The cost function of a firm is given by C(x) = 300x - 10x^2 - 1/3x^3.

A) Find the Marginal Cost Function

B) Average cost function

C) The output at which marginal cost is equal to average cost.
 
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Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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