a. Find the relative extreme values of the function. (If an answer does not exist, enter DNE.)

f(x,y) =y³x²18x12y

relative maximum?relative minimum?

b. In a laboratory test the combined antibiotic effect ofxmilligrams of medicine A andymilligrams of medicine B is given by the function

f(x,y) =xy2x²y²+143x+57y

(for0x55, 0y60).

Find the amounts of the two medicines that maximize the antibiotic effect.

?mg of drug A

? mg of drug B