A consumers utility function is given by

The consumer has a budget of £480, the price of good X and good Y are £8 and £16 per unit.

Using the Lagrange multiplier method, identify the quantities of X and Y the consumer will purchase in order to maximise their utility?

This is what I have so far...

Px =8 Py=16 B=480

Maximise

subject to constraint 8X + 16Y = 480

Partially differentiating gives

=

(1)

=

(2)

= 8X + 16Y – 480 (3)

I’ve then set these 3 equations equal to zero, in order to solve them.

However I’m uncertain as to whether I have to multiply equation (1) which would give me

and then set this equal to equation 2 ?

Or do I just divide equation (1) by equation (2) ?