An entrepreneur wants to make money selling flags for the World Cup. She must order the...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
An entrepreneur wants to make money selling flags for the World Cup. She must order the flags in advance. Let uo denote the quantity of flags she orders ahead of time. The demand for flags, denoted by w, is not known until the world cup begins. We will model this uncertainty by making w a random variable. Let u, denote the quantity of flags actually sold; this can be viewed as a decision variable whose value is chosen by the entrpreneur after she has some concrete idea of the demand (observation). Obviously, u₁ cannot exceed the stock uo, nor can it exceed the demand w. The entrepreneur can purchase flags at ore per flag and sell them for Be. The factory will repurchase left-over flags at ye per flag. Naturally, 0<7<a<B. (1) Model this problem as a two-stage problem of stochastic programming with cost function f(uo, u₁, w). Be careful to identify the constraints properly and to incorporate them into f with +00. (2) Determine the cost expression (uo, w) := infu, f(uo, u₁, w). Draw a graph showing how (20₁6) typically looks as a function of up for a fixed value of w. Do this also for o(uo, w) as a function of w for to fixed. (3) Suppose, for the sake of simplicity, that is uniformly distributed on the interval [0, 4]. An expression p(w) has expected value Ew {x(w)} = = "* (w)dw. Using this, derive a formula for (uo): E{(uo, w)}. Draw a graph showing the shape of (4) Determine the optimal amount to that should be ordered in advance if y=1, o = 2, 3=5,= 100. (5) Redo part (3), assuming that there are just three possible outcomes of demand w = 30, w = 50 and 70 (just to put numbers on "low", "medium" and "high", respectively) with equal probability. (Hint: First look at uo € [30, 50), and so forth.) 13 (6) Redo part (4) under the discrete probability distribution of part (5). (7) Under both the continuous uniform probability distribution and the discrete probability distribu- tion, the expected value of w is û 50. Suppose the entrepreneur approached the situation by assuming in advance that the demand would indeed be 50, in order to simplify the model to a deterministic problem. How much of a difference might this make to her profit potential when compared to the two probability scenarios? An entrepreneur wants to make money selling flags for the World Cup. She must order the flags in advance. Let uo denote the quantity of flags she orders ahead of time. The demand for flags, denoted by w, is not known until the world cup begins. We will model this uncertainty by making w a random variable. Let u, denote the quantity of flags actually sold; this can be viewed as a decision variable whose value is chosen by the entrpreneur after she has some concrete idea of the demand (observation). Obviously, u₁ cannot exceed the stock uo, nor can it exceed the demand w. The entrepreneur can purchase flags at ore per flag and sell them for Be. The factory will repurchase left-over flags at ye per flag. Naturally, 0<7<a<B. (1) Model this problem as a two-stage problem of stochastic programming with cost function f(uo, u₁, w). Be careful to identify the constraints properly and to incorporate them into f with +00. (2) Determine the cost expression (uo, w) := infu, f(uo, u₁, w). Draw a graph showing how (20₁6) typically looks as a function of up for a fixed value of w. Do this also for o(uo, w) as a function of w for to fixed. (3) Suppose, for the sake of simplicity, that is uniformly distributed on the interval [0, 4]. An expression p(w) has expected value Ew {x(w)} = = "* (w)dw. Using this, derive a formula for (uo): E{(uo, w)}. Draw a graph showing the shape of (4) Determine the optimal amount to that should be ordered in advance if y=1, o = 2, 3=5,= 100. (5) Redo part (3), assuming that there are just three possible outcomes of demand w = 30, w = 50 and 70 (just to put numbers on "low", "medium" and "high", respectively) with equal probability. (Hint: First look at uo € [30, 50), and so forth.) 13 (6) Redo part (4) under the discrete probability distribution of part (5). (7) Under both the continuous uniform probability distribution and the discrete probability distribu- tion, the expected value of w is û 50. Suppose the entrepreneur approached the situation by assuming in advance that the demand would indeed be 50, in order to simplify the model to a deterministic problem. How much of a difference might this make to her profit potential when compared to the two probability scenarios?
Expert Answer:
Answer rating: 100% (QA)
This problem can be modeled as a twostage stochastic programming pr... View the full answer
Related Book For
Introduction to Operations Research
ISBN: 978-1259162985
10th edition
Authors: Frederick S. Hillier, Gerald J. Lieberman
Posted Date:
Students also viewed these mathematics questions
-
Refer to the section on The Virtual Office. What do you think will be the long-term impact of the mobile office on job satisfaction and performance? If you were a manager, how would you maximize the...
-
A professor has 21 students in her class. Each student will receive a grade of A, B, C, D, or F. (a) In how many ways might the professor assign a grade of A, B, C, D, or F to each of the 21 students...
-
Grade inflation is widespread; college students receive higher grades on tests and exams today for work that would have received lower grades in the past. One recent study found that 41 percent of...
-
Describe the process of testing software developed using both top-down and bottom-up development order. Which method results in the fewest resources required for testing? What types of errors are...
-
How do employees overstate legitimate expenses on their expense reports?
-
Jacob would like your advice for the coming tax year. Assume Jacob provides more than half the support for the following individuals, none of whom qualified as a member of Jacobs household: Cousin ...
-
Advantage Advertising, Inc., engaged in the following business transactions during November of 2010: Advantage Advertising, Inc., uses the following accounts: Cash, Accounts Receivable, Supplies,...
-
Hooke's Law for a Wire A wire of length 10 and cross-sectional Area A supports a hanging weight W. (a) Show that if the wire obeys Equation (11.7), it behaves like a spring of force constant AY/lo,...
-
Granite Furniture Store has the following sales forcast for the first 4 months of the year. In month one, Granite generated $45,000 in cash sales and $200,000 in credit sales. In month two Granite...
-
Selected transactions completed by Equinox Products Inc. during the fiscal year ended December 31, 2014, were as follows: a. Issued 15,000 shares of $20 par common stock at $30, receiving cash. b....
-
or difficulty in formulating the research problem in the global marketing research effort is the unfamiliarity with the ___________________ Why we fail to recognize the research problem in global...
-
Watch a presentation or meeting in person or online. Identify audience reactions by observing each person carefully. Would you describe anyone as hostile, skeptical, or laid-back? What about their...
-
In this chapter, you read that ghosting happens on both sides of the selection process. What is your experiencein your personal or your professional lifewith being ghosted? How did you feel at the...
-
Think about an interview during which you didnt do as well as you had hoped. Dont spend too much time fretting about what went wrong. Instead, visualize a do-over: imagine watching a movie of...
-
Assume that your favorite company has invited you to an interview. To prepare for the interview, research the company by reviewing its website, reading news stories, and exploring websites like...
-
Before you do this exercise, complete Exercise in the previous section, Reflecting on Your Communication and Character Development. After youre satisfied with your review, ask two friends, family...
-
We want to use a Riemann sum with right endpoints to approximate the value of the definite integral Lor sin (27) dz a) If you divide the interval [4,6] into 3 sub-intervals of equal length, you get 3...
-
Write a function that reads a Float24_t value: Float24_t float24_read(void) A legitimate float24 value string is of the form: "mantissabexponent" where the mantissa (m) and the exponent (e) may have...
-
Consider the Reliable Construction Co. bidding problem discussed in Sec. 28.1. The spreadsheet model is available on this website. The parameter analysis report generated in Sec. 28.7 (see Fig....
-
A county chairwoman of a certain political party is making plans for an upcoming presidential election. She has received the services of six volunteer workers for precinct work, and she wants to...
-
Consider the following linearly constrained convex programming problem: Maximize f(x) = 3x1 x2 + 40x1 + 30x2 4x21 x41 3x22 x42, Subject to 4x1 + 3x2 12 x1 + 2x2 4 and x1 0, x2 0.
-
The load resistor in the NMOS inverter in Figure \(16.3(\mathrm{a})\) is \(R_{D}=40 \mathrm{k} \Omega\). The circuit is biased at \(V_{D D}=3.3 \mathrm{~V}\). (a) Design the transistor...
-
The inverter circuit in Figure 16.3 (a) is biased at \(V_{D D}=3.3 \mathrm{~V}\). Assume the transistor conduction parameter is \(K_{n}=50 \mu \mathrm{A} / \mathrm{V}^{2}\). (a) Let \(R_{D}=100...
-
(a) Redesign the resistive load inverter in Figure 16.3 (a) so that the maximum power dissipation is \(0.25 \mathrm{~mW}\) with \(V_{D D}=3.3 \mathrm{~V}\) and \(v_{O}=0.15 \mathrm{~V}\) when the...
Study smarter with the SolutionInn App