Solve the following problem using the graphical method. Choose your variables, w

Question

Solve the following problem using the graphical method. Choose your variables, write the objective function and the constraints, graph the constraints, shade the feasibility region, label all corner points, and determine the solution that optimizes the objective function.

3) In how many different ways can five people be seated in a row if two of them insist on not sitting next to each other?

4) A team plays 15 games a season. How many ways are there to end up with 6 wins and 9 losses for the season.

5) A batch contains 10 transistors of which three are defective. If three are chosen, in how many ways can one get two defective?

Explanation / Answer

3.

Total number of ways that 5 people can sit anywhere = 5! = 120

Number of ways that 2 of them seat together = 4! 2! = 48

Number of ways that 2 of them not seat togather = 120-48 = 72

4.

Total number of games = 15

If it end up with 6 win then it means it end up with 9 losses.

This is same as we need to chosse 6 out of 15 or choose 9 out of 15

therefore total number of ways = 15C6 = 15C9 = 5005 ways

5.

Total number of transistors = 10

# of defective = 3

# of non defective = 10-3 =7

Therefore number of ways to get 2 defective = (3C2)*(7C1) = 3*7 = 21

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