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Nate enjoys skiing and curling during winter times. His utility function of the two sports is represented by a nice smooth utility function: ( 1

Nate enjoys skiing and curling during winter times. His utility function of the two sports is represented by a nice smooth utility function:

(1,2)=(11/2+21/2)2

where 1 is the amount of time he spends on curling and 2 is the amount of time he spends on skiing.

A new resort has opened and offers both sports. The price of curling is $10 per hour and the price of skiing is $30 per hour. Sean has a budget of $70 to spend on the two sports. What is Nate's optimal choice?

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