You Have $5 to Spend on Any Combination of Goods

You have $5 to spend on any combination of goods A and
A.The utility maximizing combination here is to buy 1 of A and 3 of
B.Are you maximizing your utility? If so,explain why.If not,what combination of goods should you buy?
(a)The completed table:

(b)If you purchase 2 of A and 1 of B you are not maximizing your utility.To see why not,use the utility maximizing rule.For good A compute MU_A/P_A = 7 and for good B compute MU_B/P_B = 30.Since MU_B/P_B > MU_A/P_A you are not at a utility maximizing combination of goods;you should reallocate your $5 and buy more B and less
B.The price of good A is $2 and the price of good B is $1.You have calculated the following utility values for yourself:

(a)Fill in the empty columns of the table.
(b)You have purchased 2 units of good A and 1 unit of good
B.With this latter combination we see that MU_A/P_A = 8 = MU_B/P_B and we have satisfied the utility maximizing rule.