Owen is working two summer jobs, making $6 per hour walking dogs and making $11 per hour landscaping. In a given week, he can work a maximum of 14 total hours and must earn no less than $110. Also, he must work a maximum of 5 hours walking dogs and at most 11 hours landscaping. If xx represents the number of hours walking dogs and yy represents the number of hours landscaping, write and solve a system of inequalities graphically and determine one possible solution.

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.