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A utility-maximizing consumer who consumes quantity x and y of two goods has a quadratic utility...

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Basic Math

A utility-maximizing consumer who consumes quantity x and y oftwo goods has a quadratic utility function given byUx,y=x+y-0.05x2-0.05y2subject to

2x+5y=128

Where $128 is the consumer’s budget and the prices of the twogoods 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?

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