Question
Solve the optimization problem.
Minimize F = x^2 + y^2 with x + 2y = 15.
Thank You for the help!!
Minimize F = x^2 + y^2 with x + 2y = 15.
Thank You for the help!!
Answers
Damon
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
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
Jerry
Wow thank you so much!!!!