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Set up the maximization problem and the accompanying

Hugo's utility function for food and shelter is defined by F 2 S 3 . The price of food is $1 per unit and the price of shelter is $10 per unit. Hugo's Income is $100. Food and Shelter may be purchased in fractions.

Set up the maximization problem and the accompanying Lagrangian.
Are Hugo's preferences convex? Justify your answer.
How much food and shelter will Hugo consume?
Suppose the price of food increases to $1.50. How much food and shelter will Hugo now consume?
What is the income effect versus the substitution effect on F from the price change? Depict the two effects on a graph.

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