Set up the constrained optimization problem using a Lagrangian function find the optimal quantity consumed of goods 1 and 2.Check that the second order condition is also satisfied

onsider a household's utility function u = 8(91 -1) (92 -1) 3/4 here q; (i = 1,2) is quantity consumed of good i . Suppose unit price good 1 and good 2 are $5 and $4 , respectively. The budgeted income the household is $129. By setting up a constrained optimization problem and using a Lagrangian function find the optimal quantity consumed of goods