I’m working on a micro economics question and need an explanation to help me learn.

Question 1

Suppose a consumer’s utility function is given by ??(?? . The price of good1, ??2) = ??1· ??22 is given by ?? and income .2 = 1 ?? = 12- Find the optimal bundle that maximizes the consumer’s utility in three differentprice situations- Price of good 1: ??1 = 4- Price of good 1: ??1 = 3- Price of good 1: ??1 = 1- Plot the optimal bundles in the three cases found above to obtain the price offercurve (set good 1 on the x-axis and good 2 on the y-axis)