Explanation Formula used: “If u and v are differentiable functions, then ∫ u d v = u v − ∫ v d u .” Definition used: Improper integral: “If f is continuous on [ a , ∞ ) , then ∫ a ∞ f ( x ) d x = lim b → ∞ ∫ a b f ( x ) d x . If it exists and finite, then it is converges otherwise diverges.” Theorem used: Fundamental Theorem: “Let f be a continuous function on [ a , b ] . If F is anti-derivative of f on [ a , b ] , then ∫ a b f ( x ) d x = F ( b ) − F ( a ) .” Calculation: The expected sales lost per period is given by E = ∫ B ∞ ( y − B ) k 2 B e − k y 1 − e − k B d y , where B is the base stock level and k is a positive constant. In order to find the expected sales value, evaluate the above integral. That is, E = ∫ B ∞ ( y − B ) k 2 B e − k y 1 − e − k B d y = lim b → ∞ ∫ B b ( y − B ) k 2 B e − k y 1 − e − k B d y ( ∵ Definition used ) = k 2 B 1 − e − k B lim b → ∞ ∫ B b y e − k y d y − k 2 B 2 1 − e − k B lim b → ∞ ∫ B b e − k y d y = k 2 B 1 − e − k B lim b → ∞ [ − y

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Chapter 8.4, Problem 48E

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To find: The value of expected sales lost.

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Chapter 8.4, Problem 47E

Chapter 8.4, Problem 49E

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Ch. 8.1 - YOUR TURN 1 Find Ch. 8.1 - YOUR TURN 2 Find Ch. 8.1 - YOUR TURN 3 Find Ch. 8.1 - YOUR TURN 4 Find . Ch. 8.1 - YOUR TURN 5 Find Ch. 8.1 - Prob. 1WE Ch. 8.1 - Find the following. W2. Ch. 8.1 - Find the following. W3. Ch. 8.1 - Find the following. W4. Ch. 8.1 - Use integration by parts to find the integrals in...

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