The production function of a firm is Q(x, y) = x+y, where x and y are the quantities employed of each productive factor. The total cost function is: C(x, y) = 10x + 2xy + 4y² 2.1 What would be the amount of productive factors that the company must use to the total cost is minimal, under the assumption that the company wishes to maintain its production level of 3 units? What is the minimum total cost? 2.2 If the company could produce 4 units, how would the minimum cost be affected? Justify whether the company would benefit from this availability additional.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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The production function of a firm is Q(x, y) = x+y, where x and y are the quantities
employed of each productive factor. The total cost function is: C(x, y) = 10x + 2xy + 4y²
2.1 What would be the amount of productive factors that the company must use to
the total cost is minimal, under the assumption that the company wishes to maintain
its production level of 3 units? What is the minimum total cost?
2.2 If the company could produce 4 units, how would the minimum cost be affected?
Justify whether the company would benefit from this availability additional.
Transcribed Image Text:The production function of a firm is Q(x, y) = x+y, where x and y are the quantities employed of each productive factor. The total cost function is: C(x, y) = 10x + 2xy + 4y² 2.1 What would be the amount of productive factors that the company must use to the total cost is minimal, under the assumption that the company wishes to maintain its production level of 3 units? What is the minimum total cost? 2.2 If the company could produce 4 units, how would the minimum cost be affected? Justify whether the company would benefit from this availability additional.
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