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The production function for a firm is p(x, y) = 72x"y"", where x and y are the number of units of labor and capital utilized. Suppose that labor costs $108 per unit and capital costs $576 per unit and that the firm decides to produce 9216 units of goods. Determine the following. (a) Determine the amounts of labor and capital that should be utilized in order to minimize the cost. That is, find the values of x and y that minimize 108x + 576y, subject to the constraint 9216 - 72x"y"* = 0. x=. y=(Type exact answers in simplified form.)

The production function for a firm is p(x, y) = 72x"y"", where x and y are the number of units of labor and capital utilized. Suppose that labor costs $108 per unit and capital costs $576 per unit and that the firm decides to produce 9216 units of goods. Determine the following. (a) Determine the amounts of labor and capital that should be utilized in order to minimize the cost. That is, find the values of x and y that minimize 108x + 576y, subject to the constraint 9216 - 72x"y"* = 0. x=. y=(Type exact answers in simplified form.)

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.1: Quadratic Functions
Problem 6SC: A company that makes and sells baseball caps has found that the total monthly cost C in dollars of...
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The production function for a firm is p(x, y) = 72x 3/4 1/4 y where x and y are the number of units of labor and capital utilized. Suppose that labor costs $108 per unit and capital costs $576 per unit and that the firm decides to produce 9216 units of goods. Determine the following. 3/4 1/4 (a) Determine the amounts of labor and capital that should be utilized in order to minimize the cost. That is, find the values of x and y that minimize 108x + 576y, subject to the constraint 9216 – 72x y = 0. X = y = |(Type exact answers in simplified form.)
Transcribed Image Text:The production function for a firm is p(x, y) = 72x 3/4 1/4 y where x and y are the number of units of labor and capital utilized. Suppose that labor costs $108 per unit and capital costs $576 per unit and that the firm decides to produce 9216 units of goods. Determine the following. 3/4 1/4 (a) Determine the amounts of labor and capital that should be utilized in order to minimize the cost. That is, find the values of x and y that minimize 108x + 576y, subject to the constraint 9216 – 72x y = 0. X = y = |(Type exact answers in simplified form.)
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