Question

1. Maximize U(x,y)=xy subjected to Px=2, Py=8 and M=160

Answer 1

$\frac{Mux}{Muy}=\frac{Px}{Py}\\U(x,y)=x\times y$

$Mux=\frac{du}{dx}=y\\Muy=\frac{du}{dy}=x\\$

now putting values

$\frac{y}{x}=\frac{2}{8}\\2x=8y\\x=8y\\I=Px\times X+Py\times Y\\160=2\times 4y+8y\\160=8y+8y\\160=16y\\y=10$

now putting value of y in x

$x=4\times y\\x=4\times10\\x=40\\$

utility is maximum when

x=40 and y=10

$U(40,10)=40\times 10\\U=400$