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A firm produces two kinds of tennis balls, one for recreational players which sells for $2.50 per can, and one for serious players which sells for $4.00 per can. The total revenue from the sale of x thousand cans of the first ball and y thousand cans of the second ball is given by R(x, y) = 2.5x + 4y. The company determines that the total cost, in thousands of dollars, of producing x thousand cans of th first ball and y thousand cans of the second ball is given by C(x, y) = x2 - 2xy + 2y2. Find the number of each type of ball which must be produced and sold in order to maximize the profit..

A firm produces two kinds of tennis balls, one for recreational players which sells for $2.50 per can, and one for serious players which sells for $4.00 per can. The total revenue from the sale of x thousand cans of the first ball and y thousand cans of the second ball is given by R(x, y) = 2.5x + 4y. The company determines that the total cost, in thousands of dollars, of producing x thousand cans of th first ball and y thousand cans of the second ball is given by C(x, y) = x2 - 2xy + 2y2. Find the number of each type of ball which must be produced and sold in order to maximize the profit..

Calculus: Early Transcendentals
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 two kinds of tennis balls: one for recreational players, which sells for $2.50 per can, and one for serious players, which sells for $4.00 per can. The total revenue from the sale of \( x \) thousand cans of the first ball and \( y \) thousand cans of the second ball is given by: \[ R(x, y) = 2.5x + 4y \] The company determines that the total cost, in thousands of dollars, of producing \( x \) thousand cans of the first ball and \( y \) thousand cans of the second ball is given by: \[ C(x, y) = x^2 - 2xy + 2y^2 \] Find the number of each type of ball which must be produced and sold in order to maximize the profit.
Transcribed Image Text:A firm produces two kinds of tennis balls: one for recreational players, which sells for $2.50 per can, and one for serious players, which sells for $4.00 per can. The total revenue from the sale of \( x \) thousand cans of the first ball and \( y \) thousand cans of the second ball is given by: \[ R(x, y) = 2.5x + 4y \] The company determines that the total cost, in thousands of dollars, of producing \( x \) thousand cans of the first ball and \( y \) thousand cans of the second ball is given by: \[ C(x, y) = x^2 - 2xy + 2y^2 \] Find the number of each type of ball which must be produced and sold in order to maximize the profit.
Expert Solution
Step 1: Define the problem

Given that a firm produces two kinds of tennis balls, one for recreational players which sells for $2.50 per can, and one for
serious players which sells for $4.00 per can. The total revenue from the sale of x thousand cans of the first ball
and y thousand cans of the second ball is given by R open parentheses x comma y close parentheses equals 2.5 x plus 4 y

The total cost function C open parentheses x comma y close parentheses equals x squared minus 2 x y plus 2 y squared

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