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...
-
Write an SQL command to display each item ordered for order number 1, its standard price, and the total price for each item ordered.
-
The statement of cash flows for Target Corporation, a U.S. retailer, for the year ended February 2. 2008 (fiscal 2007), showed a net cash inflow from operations of $4,125, a net cash outflow for...
-
For the manufacture of vinyl chloride, assemble a preliminary database. This should include thermophysical property data, MSDSs for each chemical giving toxicity and flammability data, and the...
-
Catrina Krause is the manager of the Gordon Bagel Shop. The corporate office had budgeted her store to sell 3,000 ham sandwiches during the week beginning July 17. Each sandwich was expected to...
-
First, use both the text and Brady v US to explain plea bargaining. What features must a guilty plea have in order to be valid? Which constitutional rights are implicated by pleading guilty? (Make...
-
Laurman, Inc. is considering a new project and has provided the details of the project. The Controller has asked you to compute various capital budgeting methods to help aid in the decision to pursue...
-
In 2019 and in 2020, consumers in Dexter purchased only books and pens. The prices and quantities for 2019 and 2020 are listed in the table. The reference base period for Dexter's CPI is 2019 and...
-
Copy the figures in Problems 13-20 on your paper. Draw what you think is an appropriate tangent line for each curve at the point \(P\) by using the secant method. O P
-
Use the definition of derivative to find the derivatives in Problems 8-12. \(f(x)=44 e^{0.5 x}\)
-
Consider the sequence \(0.36,0.3636,0.363636, \cdots\). What do you think is the appropriate limit of this sequence?
-
Apportion the scholarships using Hamilton's method. Each year, 100 scholarships are awarded to the students. Use this information in Problems 33-36. A university has two colleges, Letters and...
-
The SAT scores of entering first-year college students are shown in Figure 18.21. In Problems 13-18, find the average yearly rate of change of the scores for the requested periods. Figure 18. 21 2009...
-
a. Given the following: Ca = $130, Ig = $60, Xn = $10, and G = $40, what is the economys equilibrium GDP? b. If real GDP in an economy is currently $250, will the economys real GDP rise, fall, or...
-
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.
-
Determine whether each of the following statements is true or false: Management accountants often work in cross-functional teams throughout the organization.
-
Determine whether each of the following statements is true or false: The internal audit function reports to the audit committee of the board of directors.
-
Determine whether each of the following statements is true or false: Management accountants are now more often looked upon as internal business advisors rather than bean counters recording historical...
Study smarter with the SolutionInn App