Math Problem Statement
biaya tetap sebesar 27$ dan biaya variabel perunit AVC = 1/3Q² - 8,5Q + 60. Tentukan biaya total minimum dan gambarkan fungsi biaya tersebut
Solution
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Math Problem Analysis
Mathematical Concepts
Cost Functions
Optimization
Derivatives
Formulas
Total Cost (TC) = Fixed Cost (FC) + Variable Cost (VC)
Variable Cost (VC) = AVC × Q
TC(Q) = (1/3)Q³ - 8.5Q² + 60Q + 27
First Derivative: d(TC)/dQ = Q² - 17Q + 60
Quadratic Formula: Q = (-b ± √(b² - 4ac)) / 2a
Theorems
Optimization using First and Second Derivatives
Suitable Grade Level
Undergraduate (Economics, Business, or Applied Mathematics)
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