Let u = 2x + 2Y + XY + 8 and budget constraint be 5x + 10Y = 50; (2) The marginal effect of money; (3) Maximum effect

Let u = 2x + 2Y + XY + 8 and budget constraint be 5x + 10Y = 50; (2) The marginal effect of money; (3) Maximum effect

Lagolange:
L=2X + 2Y +XY + 8 - a (5X + 10Y - 50 )
Maximize it,
2+y-5a=0
2+x-10a=0
5X + 10Y = 50
therefore
x=6
y=2
a=0.8
So when the marginal effect of money is 0.8 = Du / d money
[here the currency is 50]
Maximum effect = 36