Essentials of Business Analytics (MindTap Course List)
2nd Edition
ISBN: 9781305627734
Author: Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson
Publisher: Cengage Learning
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Textbook Question
Chapter 11, Problem 5P
Round Tree Manor is a hotel that provides two types of rooms with three rental classes: Super Saver, Deluxe, and Business. The profit per night for each type of room and rental class is as follows:
Type I rooms do not have high-speed wireless Internet access and are not available for the Business rental class. Round Tree’s management makes a forecast of the demand by rental class for each night in the future. A linear programming model developed to maximize profit is used to determine how many reservations to accept for each rental class. The demand forecast for a particular night is 130 rentals in the Super Saver class, 60 in the Deluxe class, and 50 in the Business class. Round Tree has 100 Type I rooms and 120 Type II rooms.
- a. Formulate and solve a linear program to determine how many reservations to accept in each rental class and how the reservations should be allocated to room types.
- b. For the solution in part (a), how many reservations can be accommodated in each rental class? Is the demand for any rental class not satisfied?
- c. With a little work, an unused office area could be converted to a rental room. If the conversion cost is the same for both types of rooms, would you recommend converting the office to a Type I or a Type II room? Why?
- d. Could the linear programming model be modified to plan for the allocation of rental demand for the next night? What information would be needed and how would the model change?
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Throughout, A, B, (An, n≥ 1), and (Bn, n≥ 1) are subsets of 2.
1. Show that
AAB (ANB) U (BA) = (AUB) (AB),
Α' Δ Β = Α Δ Β,
{A₁ U A2} A {B₁ U B2) C (A1 A B₁}U{A2 A B2).
16. Show that, if X and Y are independent random variables, such that E|X|< ∞,
and B is an arbitrary Borel set, then
EXI{Y B} = EX P(YE B).
Proposition 1.1 Suppose that X1, X2,... are random variables. The following
quantities are random variables:
(a) max{X1, X2) and min(X1, X2);
(b) sup, Xn and inf, Xn;
(c) lim sup∞ X
and lim inf∞ Xn-
(d) If Xn(w) converges for (almost) every w as n→ ∞, then lim-
random variable.
→ Xn is a
Chapter 11 Solutions
Essentials of Business Analytics (MindTap Course List)
Ch. 11 - Kelson Sporting Equipment, Inc., makes two types...Ch. 11 - The Sea Wharf Restaurant would like to determine...Ch. 11 - Blair Rosen. Inc. (BR) is a brokerage firm that...Ch. 11 - Round Tree Manor is a hotel that provides two...Ch. 11 - Industrial Designs has been awarded a contract to...Ch. 11 - Vollmer Manufacturing makes three components for...Ch. 11 - Photon Technologies, Inc., a manufacturer of...Ch. 11 - The Westchester Chamber of Commerce periodically...Ch. 11 - The management of Hartman Company is trying to...Ch. 11 - The employee credit union at State University is...
Ch. 11 - The Atlantic Seafood Company (ASC) is a buyer and...Ch. 11 - The Silver Star Bicycle Company will manufacture...Ch. 11 - The Clark County Sheriff’s Department schedules...Ch. 11 - Bay Oil produces two types of fuel (regular and...Ch. 11 - Consider the following network representation of a...Ch. 11 - Refer to the transportation problem described in...Ch. 11 - Aggie Power Generation supplies electrical power...Ch. 11 - The Calhoun Textile Mill is in the process of...Ch. 11 - Refer to the Calhoun Textile Mill production...
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- Exercise 4.2 Prove that, if A and B are independent, then so are A and B, Ac and B, and A and B.arrow_forward8. Show that, if {Xn, n ≥ 1) are independent random variables, then sup X A) < ∞ for some A.arrow_forward8- 6. Show that, for any random variable, X, and a > 0, 8 心 P(xarrow_forward15. This problem extends Problem 20.6. Let X, Y be random variables with finite mean. Show that 00 (P(X ≤ x ≤ Y) - P(X ≤ x ≤ X))dx = E Y — E X.arrow_forward(b) Define a simple random variable. Provide an example.arrow_forward17. (a) Define the distribution of a random variable X. (b) Define the distribution function of a random variable X. (c) State the properties of a distribution function. (d) Explain the difference between the distribution and the distribution function of X.arrow_forward16. (a) Show that IA(w) is a random variable if and only if A E Farrow_forward15. Let 2 {1, 2,..., 6} and Fo({1, 2, 3, 4), (3, 4, 5, 6}). (a) Is the function X (w) = 21(3, 4) (w)+711.2,5,6) (w) a random variable? Explain. (b) Provide a function from 2 to R that is not a random variable with respect to (N, F). (c) Write the distribution of X. (d) Write and plot the distribution function of X.arrow_forward20. Define the o-field R2. Explain its relation to the o-field R.arrow_forward7. Show that An → A as n→∞ I{An} - → I{A} as n→ ∞.arrow_forward7. (a) Show that if A,, is an increasing sequence of measurable sets with limit A = Un An, then P(A) is an increasing sequence converging to P(A). (b) Repeat the same for a decreasing sequence. (c) Show that the following inequalities hold: P (lim inf An) lim inf P(A) ≤ lim sup P(A) ≤ P(lim sup A). (d) Using the above inequalities, show that if A, A, then P(A) + P(A).arrow_forward19. (a) Define the joint distribution and joint distribution function of a bivariate ran- dom variable. (b) Define its marginal distributions and marginal distribution functions. (c) Explain how to compute the marginal distribution functions from the joint distribution function.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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