Activity 1&2 - Suppose Y is a dichotomous dependent

Activity I - Suppose Y is a dichotomous dependent variable, and the data-generating process for Y can be expressed as:

Yi=0.1+0.03X1i−0.02X2i+Ui

Interpret the coefficients on X1 and X2

Activity II - Suppose you are trying to learn the relationship between the price you charge for your product and the likelihood of purchase by individuals offered that price. You offer your product online and for one month have randomly posted prices between $10 and $30. Using data on purchases and prices, you get the following estimates for a linear probability model:

Purchasei=1.7−0.06×Pricei

You are interested in the effect of a $20 price increase (i.e., moving from the lowest price to the highest) on the likelihood of Purchase. Why is answering this question problematic using this model?