Solve this linear programming problem using the simplex...

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Solve this linear programming problem using the simplex method. 2. –/6 points
My NotesAsk Your Teacher Ellen must take 4 courses this semester. She has a list of 6 math courses and 5 science courses to from which to choose. (a) Initially Ellen is under the impression that she can simply take any four of the courses on the list. If this was the case, how many different ways could Ellen select the four courses? (b) Ellen's boyfriend tells her that he thinks that she must choose 2 math courses and 2 science courses to meet her degree requirements. If this is true, how many different ways can she select the four courses? (c) Ellen's speaks to her advisor and finds out that her program actually only requires that at least one of her four courses be a math course. Knowing this, how many different ways can she select the four courses? 3. –/6 points My NotesAsk Your Teacher There are 143 good football players in the state of Ohio. The Bears and Packers have each made up a scouting list, but 87 of these players are not on either list. The Bears' list includes
14 players that are not on the Packers' list, and the Packers' list includes 10 players who are not on the Bears' list. How many players are on the Bears' scouting list? How many players are on the Packers' scouting list? 4. –/12 points My NotesAsk Your Teacher Use the simplex method to find the maximum value of P = 16x + 7y + 10z subject to these constraints: 12x + 6y + 6z ≤ 960 24x + 6y + 6z ≤ 1500 8x + 8y + 4z ≤ 900 4x + 2y + 4z ≤ 400 and the usual constraints x ≥ 0, y ≥ 0, z ≥ 0 The maximum value of P is and this occurs when x = and y = and z = . There is one slack variable with a non-zero value when the optimal solution is achieved. This slack variable is the slack variable introduced in constraint number in the list of constraints (above), and the value this slack variable has when the optimal solution is achieved is . 5. –/4 points My NotesAsk Your Teacher Bill and Sue are playing a game they call Fuddleball. To win a game a player must score 2 consecutive points or a total of 3 points altogether. Draw a tree diagram to represent all the possible outcomes for their game of Fuddleball in which your tree records the winner of each point. How many outcomes are there in your tree? How many outcomes are there in which the winner of the first point ends up losing the game? 6. –/4 points My NotesAsk Your Teacher If people are classified by height into 7 different catagories, by weight into 4 different catagories, by eye color into 3 catagories, by sex into 2 catagories, and by ethnic group into 5 catagories, then how many different categories of people are there if people are classified according to all of the above? 7. –/4 points

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