ecop3

[9:18 AM, 10/23/2021] Flo: Choose a Company's name and background/profile? What is the nature of the business or service provided by the organization? What is its history and mission? How is this organization being affected by climate change? Does the firm/organization have a diversity and inclusion program in place? Is gender equity being addressed? What is the female manager count?

describe the climate change issue being faced by the focal organization; what the current strategic responsiveness have been, and any reported faces of change (Spector, 2013). If a sustainability program already in place, you can, in addition, draw on Benn et al (2019) Phase Models and Phases to understand where the organization is, in terms of integration models and level of engagement in CS.

Based on your theoretical analysis, what course of action do you recommend that the organization take? Which strategic responsiveness (see Spector, 2013; from Building a vocabulary of change, to key theoretical approaches from any or a variety of chapters in the book) would you suggest this organization follow? What recommendations do you offer to raise its gender equality, ethics and inclusive programs?

What do you foresee as the next steps the organization will need to make to move this project forward in the short term? What about the long term? What will be the major challenges and opportunities moving forward? Which phase model of integration do you now recommend the organization take, and why? (Benn et al 2019). [10:48 AM, 10/23/2021] Flo: 1, Assume you are managing a manufacturing line consisting of two workstations: Decambering and Hemming. The mean effective process time of the first machine is 15 minutes and its coefficient of variation is 1 (i.e., exponential distribution). The second machine has the same coefficient of variation, but this machine takes 14 minutes to process a part. (a) If there is an infinite buffer between the machines, compute the expected WIP, CT, and TH. (15 Points) WIP: __ TH: __ CT____

(b) Now assume that there is enough space for only 3 parts between the machines (Hint: the buffer size, b, is 3.) Recompute the expected WIP, CT, and TH. Compare with Part a. (15 Points) WIP: __ TH: __ CT: __ [10:48 AM, 10/23/2021] Flo: Consider the following highly simplified picture of the personal computer industry. A large number of price-taking firms assemble computer systems; call them computer OEMs (Original Equipment Manufacturers). Each of these firms must buy three inputs for each computer system that it sells

A variety of components that are themselves supplied competitively and collectively cost the computer OEM $ per computer. The Windows operating system, available only from Microsoft, at a price . Microsoft's marginal cost is $ a Pentium microprocessor available only from Intel, at a price a . Intel's marginal cost is $ Since each computer system requires precisely one operating system and one microprocessor, the marginal cost of a computer to an OEM is $$ + P_M + P_I$... [11:05 AM, 10/23/2021] Flo: Take two countries, Home and Foreign, that have different relative endowments of the two factors of production, capital and labor. These two factors are used in the production of two goods, airplanes, which use relatively intensively capital and textiles, which use labor relatively intensively. Assume that the Home country is relatively better endowed with capital than labor with respect to the Foreign country. Describe qualitatively and draw the appropriate graphs to illustrate the impact on the two countries' terms of trade and welfare of the following growth patterns:

(a) Increase in the capital stock in the Home country.

(b) Increase in the labor supply in the Home country.

(C)Increase in the capital stock in the Foreign country.

(d) Increase in the labor supply in the Foreign country.

Consider the following simplex tableau: Basic x1 x2 x3 s1 s2 Rhs (z) 1 2 5/4 0 s1 2 1 1 1 6 s2 2 1 1 4 As usual, empty cells contain a zero. Assume a maximization problem. Part 1.A Apply the simplex algorithm to compute an optimal solution. Always pivot in the column with largest reduced cost. Write down the optimal solution and optimal objective function value. Is the optimal solution that you found unique? Why? Part 1.B Describe all the optimal solutions to the problem. Use the final tableau of Part 1.A as a starting point. (Hint: the first step is to compute all optimal vertices. When we say "describe all solutions", we mean that you should find equations that describe them, not that you should write down all optimal points. That would be a very lengthy task, seeing as there is an infinite number of solutions.) Problem 2 Consider the following simplex tableau: Basic x1 x2 x3 x4 x5 Rhs (z) 0 -3 0 2 0 -6 x1 1 -4 2 0 x3 -6 1 3 2 x5 -1 1 5 Assume that this is a maximization problem. Part 2.A What is the current basic feasible solution and its objective function value? Is the current bfs degenerate? Part 2.B Perform one pivot. What is the new basic feasible solution and its objective function value? Did anything change with respect to the previous bfs? And with respect to the previous tableau? Part 2.C The tableau that you obtained after Part 2.B is not optimal because some reduced cost is positive. In fact, the problem is unbounded (why?). Give the equations describing a ray of the feasible region along which the objective function can be increased indefinitely. Problem 3 Consider the following LP: max x1 + 3x2 2x1 2x2 = 1 x1 + x2 5 x1, x2 0 (LP) Observe that a basic feasible solution is not readily apparent. We want to perform Phase I of the simplex method to find an initial basic feasible solution. Part 3.A Add surplus and artificial variables as needed to perform Phase I, then determine the Phase I objective function. Write the resulting LP and the corresponding initial Phase I simplex tableau. What is the basic feasible solution in this tableau? Part 3.B Perform two iterations of the simplex algorithm on the tableau obtained at the end of Part 3.A. Is Phase I completed? If we now have a basic feasible solution for the original problem, explain why and write the solution. If we do not have a basic feasible solution for the original problem, explain why. Problem 4 (Note: this problem is more difficult than the rest, and will require some serious thinking. You will not be tested on Problem 4 in the upcoming quizzes, problem sets or midterms. However it is very useful for understanding some subtleties of Phase I of the simplex method.) Suppose that we have an LP with three nonnegative variables x1, x2, x3 to which we have to apply Phase I of the simplex method to find an initial basic feasible solution. The artificial variables are labeled s1, s2, s3. After a few iterations of the simplex method in Phase I, we obtain the following optimal tableau with an objective function value of zero, where b is a parameter that will be specified later: 2 Basic x1 x2 x3 s1 s2 s3 Rhs (w) -1 -3 -1 x1 1 2 1 2 4 x2 1 1 -3 5 1 s2 b 1 1 -1 The artificial variable s2 is still basic, therefore we do not have a basis for the original problem. But the objective value of Phase I is zero, therefore a bfs for the original problem exists. Our goal is to find a basis to start Phase II of the simplex method. Part 4.A Assume b = 2. How do we proceed in this case? Determine a basis for the original problem and the corresponding tableau that can be used to start Phase II (after restoring the original objective function, which is not relevant for the purposes of this problem). (Hint: try to perform a pivot to drive the artificial variable out of the basis; this pivot may be something that you are normally not allowed to do, but notice that the basis is degenerate.) Part 4.B Assume b = 0. How do we proceed in this case? Determine a basis for the original problem and the corresponding tableau that can be used to start Phase II restoring the original objective function. (Hint: write down the equation corresponding to the last row of the tableau, and observe that this is a linear combination of the original constraints. What does this row mean in terms of the original equations?)

Production functions, inputs are perfect complements) Fine epoxy is used to produce LEDs and other electrical components. To get stable, good qualities (durability, resistance, adhesion) epoxy, the epoxy resins (R) are cured ("linked") to hardeners (H) like amines and acids, at the following fixed proportion: to produce 1 unit of final epoxy, we need to cure 2 units of R with 1 unit of H. Let be the quantity of final epoxy produced, (, ).

Then, the production function of epoxy is given by: (, ) = 1 2 min(, ), for some positive numbers and .

a. What is and ?

b. If we want to produce 10 units of the final product epoxy, what would be the least amount needed of R and H?

c. Does the production function of epoxy exhibit increasing, constant, or decreasing returns to scale? (IRS, CRS, or DRS?)

d. Draw a map of some isoquants of this production function