Suppose that you have five consumption choices: good

$.$ An indifference surface is the set of consumption choices with a CONSTANT utility. For example if

gives the same utility as

than these are both points on the same indifference surface. An indifference map is the set of all indifference surface for EVERY given utility.

Consider the following utility map:

Where

The budget constraint gives the set of possible consumption choices with a given income. If you have an income of $$926$ and the price of good

is given by

$.$ The equation for the budget line is given by:

$.$

A utility maximizing combination of goods

occurs when the surface given by the budget constraint is tangent to an indifference surface.

Find

as a function of