# Math

Solve the optimization problem.

Minimize F = x^2 + y^2 with x + 2y = 15.

Thank You for the help!!

1. 👍 0
2. 👎 0
3. 👁 303
1. x = 15 - 2y
x^2 = 225 - 60 y + 4 y^2

F = 5 y^2 -60 y + 225
dF/dy = 10 y - 60
zero when y = 6 then x = 3

is that min or max?
d^2F/dy^2 = 10 so it is min

F here = 9+36 = 45

check ends
if x = 0 y = 7.5 and F = 56 1/4
if y = 0, x=15 and F = 225
ok, done

1. 👍 1
2. 👎 0
posted by Damon
2. Wow thank you so much!!!!

1. 👍 0
2. 👎 0
posted by Jerry

## Similar Questions

1. ### Calculus

Can someone please walk me through the steps, I am just not sure what to do next. thanks Solve the optimization problem. Minimize F = x^2 + y^2 subject to xy^2 = 16 I took the derivative F = 2x + 2Y but I don't know where to go

asked by Jennifer on November 6, 2014
2. ### Calc

A 100 inch piece of wire is divided into 2 pieces and each piece is bent into a square. How should this be done in order of minimize the sum of the areas of the 2 squares? a) express the sum of the areas of the squares in terms of

asked by katie on November 16, 2010
3. ### Math

1. Use MATLAB Optimization Tool to solve the following problem: minimize [2x1^2+2x1x2+x2^2-10x1-10x2] subject to [x1^2+x2^2≤500] and [5x1-x2 ≤ -4] . 2. Please hand-check all the Kuhn-Tucker conditions for your answer.

asked by Jiya on December 13, 2015
4. ### Calculus

*Optimization problem* I'm okay at some optimization problems, but this one has me stumped. You work for a company that manufactures circular cylindrical steel drums that can be used to transport various petroleum products. Your

asked by Zared on November 29, 2012
5. ### Math

Optimization Problem A right circular cylindrical can of volume 128tπ cm^3 is to be manufactured by a company to store their newest kind of soup. They want to minimize the surface area of the can to keep costs down. What are the

asked by Kevin on March 15, 2013
1. ### Calculus

Optimization An offshore oil well is 2km off the coast. The refinery is 4 km down the coast. Laying a pipe in the ocean is twice as expensive as on land. What path should the pipe follow in order to minimize the cost?

asked by lele on November 6, 2011
2. ### HELPPP

Solve the linear programming problem by the method of corners. Minimize C = 5x + y subject to x + 3y ≥ 43 x + y ≥ 27 x ≥ 0, y ≥ 0

asked by Leah on April 18, 2011
3. ### Math

Solve the linear programming problem by the method of corners. Minimize C = 3x + 7y subject to 4x + y ≥ 39 2x + y ≥ 29 x + 3y ≥ 42 x ≥ 0, y ≥

asked by ANGELA on February 23, 2011