maximum and minimum values of a function

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HI! I am currently working on some calc3 online homework problems and this one is giving me a bit of tough time. I found the gradient of f to be <16x,10y> and the gradient of g to be <4,20>. I used this information to solve for x and y and to obtain a critical point of (3/164, 6/41). Using the critical point and the original function I obtained the min value of 9/82. I am just a little lost on how to obtain the max value. If someone could help find the max value I would greatly appreciate it!