Patrick chooses to use his time ‘free-time’: (a) working out or (b) reading. Patrick currently has 20 hours a week to allocate to these two activities. It takes Patrick 1.5 hour to work out and .5 hours to read. Patrick enjoys both activities, but he has recently focused more on improving his thought processes; therefore, he spends more time ‘reading’. Patrick feels that the optimal allocation of his time, based upon his budget constraints, is to allocate 12.5 hours to reading and 7.5 hours to working out.

(a) Draw Patrick's budget constraint and optimal consumption bundle such that the number of hours that he spends working out is on the x-axis and the number of hours that he spends on reading is on the y-axis.

(b) Patrick spends more time working out and reading and he becomes more efficient at completing both of these tasks. He can now complete a work out in an hour and he can read the same amount that he previously read in half the time. If the ratio between choosing to read or work out has not changed, please graph his budget constraint and indicate where his knew budget constraint is based upon this new information.

Please show all work for explanation purposes.