A certain country uses a progressive tax system. The amount of tax consists of a linear part proportional to the income and a nonlinear part depending on the income by a power law. The total amount of tax is determined by the formula T(W)=aW+(bW+c)p, where W is the income; p is the exponent, a,b,c are some positive numbers. At what level of income the tax rate will be minimal?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.6: Variation
Problem 13E
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A certain country uses a progressive tax system. The amount of tax consists of a linear part proportional to the income and a nonlinear part depending on the income by a power law. The total amount of tax is determined by the formula

T(W)=aW+(bW+c)p,

where W is the income; p is the exponent, a,b,c are some positive numbers. At what level of income the tax rate will be minimal?

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