Reconsider the example illustrating the use of chance constraints that was presented in Section 8.8. Suppose that after a more careful consideration of the hours required per door and window in Plant 3, H_D3 and H_W3, Wyndor management has considerably narrowed the range of what these times might turn out to be. 

a. H_D3 and H_W3 are now considered equally likely to be anywhere between 15 minutes below and 15 minutes above the original estimates of 3 hours and 2 hours, respectively. Use a chance constraint and Analytic Solver to find the solution that maximizes total profit while requiring at least a 95 percent chance of satisfying the original constraint for the third plant. 

b. Repeat part a, but now require at least a 99 percent chance of satisfying the constraint at the third plant. 

c. Now assume H_D3 and H_W3 follow the normal distribution with means equal to the original estimates of 3 hours and 2 hours, respectively, and each with a standard deviation of 0.25 hours. Use a chance constraint and Analytic Solver to find the solution that maximizes total profit while requiring at least a 95 percent chance of satisfying the original constraint for the third plant. 

d. Repeat part c, but now require at least a 99 percent chance of satisfying the original constraint at the third plant.