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.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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.
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