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Midterm_Review

Midterm_Review - MAT540 Midterm Review Chapters 1 11 12 14...

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MAT540 Midterm Review Chapters 1, 11, 12, 14, 15 Management Science Total Cost: v f vc c TC + = Total Revenue: vp TR = Total Profit: v f v f vc c vp vc c vp Z t total revenue total Z - - = + - = - = ) ( cos Break-even Point: v f c p c v Z - = = 0 Where: volume v price p t iable c t fixed c v f = = = = cos var cos Example: Fixed cost = 8,000 Variable cost = 65 Price = 180 (a) volume = 300 TC (total cost) = 27,500 (Fixed cost + volume*variable cost) TR (total revenue) = 54,000 (volume*Price) Profit = 26,500 (TR - TC) (b) volume = 69.57 tables (fixed cost/(price - variable cost)) Probability and Statistics: P(A or B) = P(A) + P(B) – P(AB) Where P(A or B) = probability event A or B or both will occur, P(A) = probability event A will occur, P(B) = probability event B will occur, P(AB) = probability that both event A and B will occur. 1

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MAT540 Midterm Review Chapters 1, 11, 12, 14, 15 Example: P(Negative Test Result or Not Pregnant) = P(Negative Test Result) + P(Not Pregnant) – P(Negative Test Result and Not Pregnant) = 16/99 + 14/99 – 11/99 = 19/99 Independent Events: A succession of events that do not affect each other. If A and B are independent, P(AB) = P(A)•P(B) Example: Flip a coin twice, the probability of a head followed by a tail is: P(HT) = P(H)•P(T) = (.5)(.5) = .25 Binomial Distribution: trials n in successes of number r trials of number n failure of y probabilit p q success of y probabilit p where q p r n r n r P r n r = = = - = = - = - 1 )! ( ! ! ) ( Example: Assume n= 20, p=0.1 P(r ≥ 5) – rejected. P(r < 5) – accepted. P(r < 5) = P(r = 0) + P(r = 1) + P(r = 2) + P(r = 3) + P(r = 4) P(r < 5) = 4 20 4 3 20 3 2 20 2 1 20 1 0 20 0 9 . 0 1 . 0 )! 4 20 ( ! 4 ! 20 9 . 0 1 . 0 )! 3 20 ( ! 3 ! 20 9 . 0 1 . 0 )! 2 20 ( ! 2 ! 20 9 . 0 1 . 0 )! 1 20 ( ! 1 ! 20 9 . 0 1 . 0 )! 0 20 ( ! 0 ! 20 - - - - - - + - + - + - + - P(r < 5) = 0.1216 + 0.2702 + 0.2852 + 0.1901 + 0.0898 = 0.9569 (accepted) P(r ≥ 5) = 1 – P(r < 5) = 1 – 0.9569 = 0.0431 (rejected) 2
MAT540 Midterm Review Chapters 1, 11, 12, 14, 15 Expected Value: E(x) = ) ( x P x Example: x P(x) x•P(x) 0 .10 0 1 .20 .20 2 .30 .60 3 .25 .75 4 .15 .60 ∑x•P(x) = 2.15 Normal Distribution: deviation dard s mean erest of value x where x z tan , , int , = = = - = σ μ σ μ Example: Note: x = 400 is to the left of the mean in following example.

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