# Maximize Values - Calculus

Find two non negative numbers x and y such that 2x+2y=500 and x^3+y^3 is maximal.

### Comments for Maximize Values - Calculus

 Apr 09, 2012 Maximize Values - Calculus by: Staff Question: Find two non negative numbers x and y such that 2x+2y=500 and x^3+y^3 is maximal. Answer: Maximize the function f(x,y) = x³ + y³ subject to the following constraint: 2x + 2y = 500 Since 2x + 2y = 500 is a linear equation, the only possible non-negative values of x and y can be are: 0 ≤ y ≤ 250 0 ≤ x ≤ 250 2x + 2y = 500 Solving for y y = 250 - x substitute 250 – x for the y value in f(x,y) f(x,y) = x³ + y³ f(x) = x³ + (250 – x)³ f(x) = 750x² - 187500x + 15625000 f(x) = 750(x – 125)² + 3906250 as you can see, once the function is expanded, it turns out to be a parabola f(x,y) will be at its minimum of 3906250 (the vertex) when x = 125 and y = 125 The question is: What is the maximum given the following constraints: 0 ≤ y ≤ 250 0 ≤ x ≤ 250 >>> the final answer is: There are two solutions: Given the constraints on the values of x and y, f(x,y) = x³ + y³ is maximized when: x = 0 and y = 250 or x = 250 and y = 0 Thanks for writing. Staff www.solving-math-problems.com

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