1. A consumer consumes two kinds of goods, namely X and Y. The total satisfaction (TU) obtained in consuming both kinds of goods is shown in the equation; (Unit of money in thousands of dollars).
TU = 10X + 24Y - 0.5X2 - 0.5Y2
TU is the total satisfaction in consuming goods X and Y
X is the number of items X consumed
Y is the number of items Y consumed
The price of item X is known to be Rp. 2 the price of item Y is Rp. 6 and the available budget for buying item X and item Y is Rp. 44

Explain it along with the formula used !
Question:
a. Determine how many goods X and the number of goods Y must be consumed so that the consumer gets maximum total satisfaction. Determine the total satisfaction that can be obtained from consuming item X and item Y.
b. If the price of item X drops from Rp. 2 to Rp. 1, determine the number of items X and the number of items Y must consume in order to obtain maximum total satisfaction. Determine the total satisfaction that can be obtained from the consumption of item X and item Y.