A utility-maximizing consumer who consumes quantity x and y of
two goods has a quadratic utility function given by
Ux,y=x+y-0.05x2-0.05y2
subject to
2x+5y=128
Where $128 is the consumer’s budget and the prices of the two
goods are, respectively, 2 and 5. Assuming marginal utilities Ux,
Uy > 0,
a. Find the quantity x and y that maximize the utility function.
b. Using bordered Hessian, check utility for a maximum.
c. What is the maximum utility of the consumer?