MATH 0180 Midterm: MATH 180 Brown Exam m180s5b
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Since124. 441 theabovesystemoflinearequations has a uniquesolution to o: o eb so it is theonlyinteriorcriticalpoint. Atlo o g ac132 8 16 24 0. Infact sincelo o is asaddle thisvaluecannotbethemaximum or minimum andthus canberuledout atthispoint. It nowbecomes a constrained maxlminproblemof f ay x 49 2y withtheconstraint guy x4y2 5 0. Since xy t o o inviewof we seethat the coefficientmatrix of eg ie r. Mtd 6 0 ht3 la 2 o di 3 112 2. Observethat xx t xy gives l 111 2 2 912kg l z d92 0. Hencethe corresponding valuesof f at all candidatepoints ofboundary are f 5a 15 f 5112 10. Alternatively we canfirstsolvefor cx. gl andthen plug in thepoints to findtheabovevalues of f i a 3 reduceto y. Bothpoints 1 2 andl l 2 leadto f x44xy42 1 8 8 15 reduceto x g ii az 2 eg. 49292 5 tr y2 1 f it for1 2 y 1.
