A firm produces a good from two raw materials X and Y which can be bought at unit prices of pX and pY , respectively. Given a quantity x of X and a quantity y of Y , the firm can produce a quantity of goods q given by the production function q(x, y) = 3x^1/3y^2/3. The firm has a budget of $1,000 with which to buy the raw materials X and Y at unit prices of $2 and $3, respectively. Find the optimal quantities x and y that maximizes production subject to the budget constraint.

A firm produces a good from two raw materials X and Y which can be bought at unit prices of pX and pY , respectively. Given a quantity x of X and a quantity y of Y , the firm can produce a quantity of goods q given by the production function q(x, y) = 3x^1/3y^2/3. The firm has a budget of $1,000 with which to buy the raw materials X and Y at unit prices of $2 and $3, respectively. Find the optimal quantities x and y that maximizes production subject to the budget constraint.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 93E

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