A survey of 42 men was taken asking about their likes of certain female names: Amy, Beth and Cindy. It was discovered that 13 men liked the name Amy, 20 of them liked Beth, 8 liked Beth but not Cindy, 13 liked Cindy but not Beth, 7 liked Amy but not Beth, 4 liked only the name Amy and 2 liked Amy and Beth but not the name Cindy. Find the following and draw the Venn Diagram corresponding to this problem.

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.)