Let Y₁ and Y₂ denote the proportions of time (out of one workday) during which employees I and II, respectively, perform their assigned tasks. The joint relative frequency behavior of Y₁ and Y₂ is modeled by the density function

f(y1,y2)=y1+y2 where 0y11,0y21

Employee I has a higher productivity rating than employee II and a measure of the total productivity of the pair of employees is 30Y₁ + 25Y₂.

1. Find the mean of this measure of productivity.

2. Find the variance of this measure of productivity.

3. Give an interval in which you think the total productivity measures of the two employees should lie for at least 75% of the days in question.