A model of mode split (with two modes) has been estimated as ln(Pija=1 Pija) 8(ta

A model of mode split (with two modes) has been estimated as ln(Pija=1  Pija) ¼ 8(ta  tb)  2(ma  mb);

where mode a is auto and mode b is public transit, t(travel time) is measured in minutes, and m (money cost) is measured in cents.

a. At what values of t a t b and ma  mb is the probability of using the auto equal to 0.5?

b. Draw the graph of Pija as a function of z ¼  8(ta  tb)  2(ma  mb).

c. What is the value of reductions in commuting time implied by the estimated mode split function? What unit of measurement did you use to express the value of time?