Average cost. A company manufacturing snowboards has fixed costs of $200 per day and total costs of $3,800 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 C ¯ x = C x / x . Find the average cost function. (C) Sketch a graph of the average cost function, including any asymptotes, for 1 ≤ x ≤ 30 (D) What does the average cost per board tend to as production increases?
Average cost. A company manufacturing snowboards has fixed costs of $200 per day and total costs of $3,800 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 C ¯ x = C x / x . Find the average cost function. (C) Sketch a graph of the average cost function, including any asymptotes, for 1 ≤ x ≤ 30 (D) What does the average cost per board tend to as production increases?
Refer to page 100 for problems on graph theory and linear algebra.
Instructions:
•
Analyze the adjacency matrix of a given graph to find its eigenvalues and eigenvectors.
• Interpret the eigenvalues in the context of graph properties like connectivity or clustering.
Discuss applications of spectral graph theory in network analysis.
Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440 AZF/view?usp=sharing]
Refer to page 110 for problems on optimization.
Instructions:
Given a loss function, analyze its critical points to identify minima and maxima.
• Discuss the role of gradient descent in finding the optimal solution.
.
Compare convex and non-convex functions and their implications for optimization.
Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qo Hazb9tC440 AZF/view?usp=sharing]
Refer to page 140 for problems on infinite sets.
Instructions:
• Compare the cardinalities of given sets and classify them as finite, countable, or uncountable.
•
Prove or disprove the equivalence of two sets using bijections.
• Discuss the implications of Cantor's theorem on real-world computation.
Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharing]
Chapter 2 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
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