show work please

6. Assume that Latisha has a budget of $64. She consumes gelato (X) and marshmallows (Y) together. Her utility function is U = X1/2Y1/2. The prices of gelato and marshmallows are Px =$8 per unit and Py =$4 per unit. (a) Based on the information above, calculate the optimal consumption bundle. (1 point) (Jaioq !) i. X = soubor ii. Y =_ (b) Now assume that Latisha's income increases to $80. Calculate the new optimal consumption (Jning !) bundle. (1 point) i. X = ii. Y = (c) Now assume that Latisha's income further increases to $96. Calculate the new optimal consumption bundle. (1 point) i. X = ii. Y = 1b