[This is 50 points and I’ll give brainliest. Let’s strengthen these Plato answers for math, eh?] Two friends worked together on an entry for a poetry contest and won; however, there is only one prize and it cannot be split. Some methods of
determining who receives the prize are given below.

Select all the fair methods for determining who receives the prize.

1. throw a stone closest to an object

2. roll a die and evaluate the outcome as either even or odd

3. ask a stranger to flip a coin

4. place both names in equal amounts into a hat and draw one without looking

5. ask a random friend to choose

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.)