A real estate investor notes that of his portfolio, 30% of his apartments are rented to families, 40% are single occupant, and 30% are rented to multiple occupants (non-families). The probability that a rent payment is late for the apartments rented by families is 0.05, while the probability rent is late for single occupants is 0.2, and 0.12 for multiple occupants. What is the probability that if a rent payment is late it is a family occupied apartment

Acaterer knows he will need 60, 50, 80, 40 and 50 dinner napkins on five successive evenings. he can purchase new napkins initially at 25 cents each, after which he can have dirty napkins laundered by a fast one-day laundry service (i.e., dirty napkins given at the end of the day will be ready for use the following day) at 15 cents each, or by a slow two-day service at 8 cents each or both. the caterer wants to know how many napkins he should purchase initially and how many dirty napkins should be laundered by fast and slow service on each of the days in order to minimize his total costs. formulate the caterer’s problem as a linear program as follows (you must state any assumptions you make): a. define all variables clearly. how many are there? b. write out the constraints that must be satisfied, briefly explaining each. (do not simplify.) write out the objective function to be minimized. (do not simplify.)