Use lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. (if an answer does not exist, enter dne.)f(x, y) = 5x2 + 5y2; xy = 1

The Lagrangian is



Set the partial derivatives equal to 0:



Notice that , or .

Since , it follows either , and so there are two critical points at (1, 1) and (-1, -1). Both of these points give the same value of . And since the Hessian matrix for is positive-definite, these points correspond to minima. has no maximum value on .

First, think of what you know. you know that the number t the end of the equation will need to be subtracted because it is the money he lost from buying the lawn mower. and your first two weeks have negative profit, so that tells you that c and d are wrong. now you can plug any of the weeks into a and b to see which one works. i'll start with plugging week 1 into a.this isn't right because it says your answer for week one should be -90.so now we need to try the same thing with b.this one got you the right answer, (sometimes if you only check with one of the weeks multiple will work so you need to check with more of the weeks, but it worked out fine here)this means that b is the correct answer.let me know if you need more clarification. i hope this : )