Question

Two drugs are being used to treat a sickness. Studies have shown that the length of the sickness can be modeled by 2(x, y) = x2 + 6y2 – 12x – 42y + 2xy + 180 where x is the amount of Drug A and y is the amount of Drug B (both in hundreds of milligrams). What amounts of Drug A and Drug B would minimize the length of the sickness? Drug A hundred mg Drug B hundred mg

Answer 1

f(x,y)=x² +6y? 12x-42y+2xy +180 fa = 2x - 12+2y Jy = 2x +12y-42 So =2, Sw=12, Sny = 2 Now for optimization Wemust have, fa=0=2x-12+2y=0......(i) Sy=0=> 2x +12y - 42 =..(i) Solving (i) and (ü) we Get x =3, y=3 Now Since fly-fry = 20 >0 and ſw=2> 0 at (3,3) Hence (3,3) will give the Minimum DrugA =3 hundredmg DrugB=3 hundredmg