A small company produces three types of goods. The profit function is given by P(x, y, z) = 5 ln(x + 1) + 8 ln(y + 1) + 12 ln(z + 1), where x, y and z are the monthly quantities sold of goods of type 1, 2 and 3, respectively. The production cost per unit of type 1 goods is $ 10; the cost per unit of type 2 goods is $ 15; the cost per unit of type 3 goods is $ 30. The monthly budget of the company (which is spent entirely on the 3 types of goods) is $2945. How should the budget be allocated to maximize the monthly profit? ● ● You do not need to investigate boundary points and it suffices to find a relative maximum. You might want to work with the variables x = x + 1, y = y + 1 and z = z + 1 to make the calculations easier.

A small company produces three types of goods. The profit function is given by P(x, y, z) = 5 ln(x + 1) + 8 ln(y + 1) + 12 ln(z + 1), where x, y and z are the monthly quantities sold of goods of type 1, 2 and 3, respectively. The production cost per unit of type 1 goods is $ 10; the cost per unit of type 2 goods is $ 15; the cost per unit of type 3 goods is $ 30. The monthly budget of the company (which is spent entirely on the 3 types of goods) is $2945. How should the budget be allocated to maximize the monthly profit? ● ● You do not need to investigate boundary points and it suffices to find a relative maximum. You might want to work with the variables x = x + 1, y = y + 1 and z = z + 1 to make the calculations easier.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 94E

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