The Wittgenstein family's utility function is given byU(x,y,z) = 4ln(x) + 7ln(y) +14ln(z),wherex, yandzare the quantities ofX-merch,Y-merch andZ-merch, that the family consumes per month, respectively.

The prices ofX-merch,Y-merch andZ-mercharepx = $5, py = $10andpz = $30per unit, respectively.

(a) (4 pts)Find the Wittgenstein family's maximum monthlyXYZutility, given that their monthlyXYZbudget isB = $1500.

(b) (2 pts)By how much will the Wittgenstein family have to increase theirXYZbudget, if they want to increase theirXYZutility by3utils (units of utility) from the number you found in part(a)?

(c) (1 pt)Use the envelope theorem (and linear approximation) to estimate the change to the Wittgenstein family's maximum utility from part (a) if the price ofX-merch increases to$5.75.

For full credit show your work.