Analytics for Managerial Decision-Making

 

Part I

1. (10 points) Chapter 1 Problem 8. Skip part (c). For part (d), you may consider using the Linear Programming module of POM-QM.
Recall the production model from Section 1.3:

Suppose the firm in this example considers a second product that has a unit profit of $5 and requires 2 hours of production time for each unit produced. Use y as the number of units of product 2 produced.
a. Show the mathematical model when both products are considered simultaneously.
b. Identify the controllable and uncontrollable inputs for this model.
c. Draw the flowchart of the input–output process for this model (see Figure 1.5).
d. What are the optimal solution values of x and y?
e. Is the model developed in part (a) a deterministic or a stochastic model? Explain.

2. (15 points) Ponderosa Development Corporation (PDC) is a small real estate developer that builds only one style house.

• The selling price of the house is $115,000.
• Land for each house costs $55,000 and lumber, supplies, and other materials run another $28,000 per house.
• Total labor costs are approximately $20,000 per house.
• Ponderosa leases office space for $2,000 per month. The cost of supplies, utilities, and leased equipment runs another $3,000 per month.
• The one salesperson of PDC is paid a commission of $2,000 on the sale of each house. PDC has seven permanent office employees whose monthly salaries are given in the table below:
Employee Monthly Salary
President $10,000
VP, Development 6,000
VP, Marketing 4,500
Project Manager 5,500
Controller 4,000
Office Manager 3,000
Receptionist 2,000

a) Identify all costs and denote the marginal cost and marginal revenue for each house.
b) Write the monthly cost function c (x), revenue function r (x), and profit function p (x).
c) What is the breakeven point for monthly sales of the houses?
d) What is the monthly profit if 12 houses per month are built and sold?
e) Determine the BEP for monthly sale of houses graphically.

3. (15 points) Chapter 1 Problem 10
A retail store in Des Moines, Iowa, receives shipments of a particular product from Kansas City and Minneapolis. Let
X=5 number of units of the product received from Kansas City
Y= 5 number of units of the product received from Minneapolis
a. Write an expression for the total number of units of the product received by the retail store in Des Moines.
b. Shipments from Kansas City cost $0.20 per unit, and shipments from Minneapolis cost $0.25 per unit. Develop an objective function representing the total cost of shipments to Des Moines.
c. Assuming the monthly demand at the retail store is 5000 units, develop a constraint that requires 5000 units to be shipped to Des Moines.
d. No more than 4000 units can be shipped from Kansas City, and no more than 3000 units can be shipped from Minneapolis in a month. Develop constraints to model this situation.
e. Of course, negative amounts cannot be shipped. Combine the objective function and constraints developed to state a mathematical model for satisfying the demand at the Des Moines retail store at minimum cost.

4. (10 points) Solve the linear program that you obtained in part (e) of Chapter 1 Problem 10 (Question #3) using the Linear Programming module of POM-QM. Report the optimal values of the decision variables (x and y) and also the optimal objective function value.

5. (10 points) Chapter 1 Problem 16

Financial Analysts, Inc., is an investment firm that manages stock portfolios for a number of clients. A new client is requesting that the firm handle an $800,000 portfolio. As an initial investment strategy, the client would like to restrict the portfolio to a mix of the following two stocks:

Let
X= 5 number of shares of Oil Alaska
Y= 5 number of shares of Southwest Petroleum

6. (15 points) Solve the linear program that you obtained in Chapter 1 Problem 16 (Question # 5) using the Linear Programming module of POM-QM. Report the optimal values of the decision variables (x and y) and also the optimal objective function value. Were any of the possible funds available for investment in Oil Alaska or Southwest Petroleum left unused?

7. (15 points) A snack food manufacturer buys corn for tortilla chips from two cooperatives, one in Iowa and one in Illinois. The price per unit of the Iowa corn is $6.00 and the price per unit of the Illinois corn is $5.50.
a. Define variables that would tell how many units to purchase from each cooperative.
b. Develop an objective function that would minimize the total cost.
c. The manufacturer needs at least 12,000 units of corn. The Iowa cooperative can supply up to 8,000 units, and the Illinois cooperative can supply at least 6,000 units. Develop constraints for these conditions.

Part II

8. (10 points) Accounts of several successful Operations Research applications in the industry can be found at O.R. & Analytics Success Stories (https://www.informs.org/Impact/O.R.-Analytics-Success-Stories) Select an industry, or function, or benefit that interests you, then pick an interesting success story and develop a short abstract on the application. Clearly specify (a) the industry/function/benefit you selected, and (b) the title of the success story. Your abstract should not exceed 150 words.

 

 

Sample Solution

What was “new” about the New South? The accompanying will talk about what, on the off chance that anything was new about the New South that rose in the United States after 1877. Before the American Civil War the old South had overwhelmingly been an agrarian economy in which blacks were slaves who had taken a shot at the cotton ranches, plants, or had been residential hirelings. Cotton had been the real ware of the economy, which had chiefly been traded to Britain. The American Civil War had been battled about the issue of subjugation and whether the Southern States reserved the privilege to surrender from the United States to safeguard the establishment of bondage (Hobsbawm, 1975 p.184). The Civil War conveyed social and monetary changes toward the South. Its cotton trades had been definitely decreased, its horticultural and mechanical yield declined strongly, while quite a bit of its framework was decimated. Amid the common war President Lincoln had declared the liberation everything being equal, while blacks had battled with unique excellence on the Union side. The obliteration conveyed toward the South by the common war implied that a time of recreation was required a short time later. Driving white Southerners, for example, Henry Grady required a New South. The blacks that were liberated, because of the Confederate States losing the common war, likewise foreseen a New South. The blacks in the Southern States anticipated that their lives should be better after the Union’s triumph and the period of remaking. In numerous regards solid contentions can be exacerbated that their lives showed signs of improvement. Du Bois for one battled that blacks “had battled bondage to spare popular government and afterward lost vote based system in another and vaster subjugation” (Du Bois, 1935 Chapter 1). The consequence of the American Civil War in principle was that the four and a half million blacks in the United States were all free and equivalent with the white populace. In any case, the finish of the Reconstruction made those equivalent rights a joke in the New South (Brogan, 1999, p.348). That the New South was not another spot for the better for its dark populace was because of the manner by which the American Civil War finished. Lincoln’s death was the South’s retribution for losing the War. Lincoln’s successor, Andrew Johnson was less equipped for guaranteeing that the South changed in manners that profited its dark populace. From his administration onwards, the North did next to no to guarantee Southern blacks had any significant rights (Brogan, 1999, p.348). Southern blacks were just ready to practice their political rights while the Union powers stayed in the South, those rights stopped to exist as a general rule once the South was left to run itself. The concealment of Southern blacks was ostensibly more awful once they had been formally liberated than when they had been slaves. Racial segregation, the dread of brutality and destitution implied that the New South was no superior to anything the Old South had been (Hobsbawm, 1975, p.143). Neither the South when all is said in done or its curbed dark populace specifically, picked up as much from the United States fast industrialisation from the 1870s onwards as the North did (Hobsbawm, 1987, p.35). In the New South there was a powerful urge among the crushed Confederate States to make its dark populace subject to its exacting political and financial controls for whatever length of time that conceivable. The abrogation of subjection had not seen the finish of the cotton ranches. In any case, employments and better pay were given to the whites as opposed to blacks. Blacks were given the least paid employments and they could be rebuffed for not taking them. For some blacks the freshness of the New South was the expanded cruelty of the separation they were exposed to. While the whites in the New South had been unfit to vanquish the Union amid the American Civil War, they were in a situation to make life extremely upsetting for the dark populace of the New South. Much separation was given legitimateness through the ‘Dark Codes’ of the Southern councils that seriously confined the privileges of previous slaves. Subjection had, in numerous regards, been reestablished in a more subtle structure (Brogan, 1999, p.352). Those blacks that endeavored to practice their lawful rights found legitimate and political impediments set before them, which adequately denied them of each one of those rights. They likewise confronted viciousness and terrorizing all the time (Bradbury and Temperley, 1998, p.153). The Southern states had the capacity to keep the Constitutional Amendments that nullified bondage and gave liberated slaves their rights having a positive effect as they were in charge of their authorization, instead of the national government (Murphy et al, 2001, p.315). States, for example, Louisiana had no goal of giving blacks any rights on the grounds it was unlawful to do as such (Du Bois, 1935, p.454). A progression of measures which were known as Jim Crow laws were utilized by the Southern States to isolate and stifle their dark populaces. Despite the fact that they guaranteed the isolated administrations were of equivalent quality, this was a hoax to pardon ignoring their dark networks (Cobb, 1992). Generally speaking Jim Crow Laws deferred the monetary advancement of the New South, while they systematized racial separation and isolation. The expense of giving isolated administrations brought down the nature of training, lodging, and transport in the New South. Isolation had even been embraced by the Supreme Court insofar as administrations were of equivalent quality, which few tried to check. Such separation was in opposition to the manner in which Henry Grady trusted the New South ought to have created. Grady contended that the most ideal approach to industrialize the New South was to regard blacks as equivalent accomplices instead of inferiors. In this manner social equity and fairness were similarly as vital as capital and apparatus in structure the New South (Mauk and Oakland, 1995 p. 108). Grady trusted that the New South would be the ideal majority rules system as long blacks were dealt with similarly. The common war had been an open door for the South to stop its obsolete dependence on bondage and cotton (Harris, 1890 p. 15). Isolation, just as being ethically faulty, kept the South generally poor and in reverse in connection to the remainder of the nation (Hobsbawm, 1975 p.184). Destitution was another element of the New South. Destitution incomprehensibly enough had not been an issue for blacks in the South when they had been slaves. In spite of the fact that, they had no opportunity, slaves were furnished with essential dimensions of convenience and nourishment, on the sensible premise that undesirable slaves did not fill in just as solid ones. Southern slave proprietors had commonly treated their slaves all around ok for their numbers to increment at a similar rate as the white populace (Bradbury and Temperley, 1998 p. 153). Protectors of subjugation had kept up that it kept the Southern states monetarily aggressive, kept the dark populace at subsistence, while guaranteeing that every white man could discover paid work (Brogan, 1999, p.371). Neediness, as liberated slaves found to their expense, was as prohibitive of their opportunity as real shackles had been. Liberated slaves needed to contend with whites to pick up employments. Destitution was firmly connected with racial separation, in that whites were given better employments and better working conditions, notwithstanding when there were better-qualified blacks to carry out the responsibilities. Separation in the arrangement of instruction, lodging and restorative consideration likewise added to keep the blacks subdued and in neediness (Cobb, 1992). Blacks were disappointed by their neediness, while escape clauses were utilized to guarantee that poor whites kept the vote (Hobsbawm, 1987, p.24). Another new component of the New South was the expanded dimensions of urbanization. Urban areas, for example, New Orleans and Birmingham expanded in size amid the recreation time. The urbanization of the New South was aftereffect of the modern development supported by the Southern states and the movement of individuals attempting to escape rustic neediness. Moving to the urban communities did not decrease racial segregation and it scarcely expanded open doors for dark individuals. Birmingham was the main city to accomplish industrialisation on a noteworthy scale in the New South. The South was monetarily kept down by its intentionally uneducated blacks and its under instructed whites (Brogan, 1999, p.372). Southern blacks had additionally moved to northern urban areas, for example, New York to build their chances and to escape racial separation. The North was as yet inclined to such separation regardless of whether it gave more noteworthy chance and blacks confronted lower dangers of brutality. The Southern states had been spurred to institute the ‘Dark Codes’ to confine relocation to both Southern and Northern urban communities (Brogan, 1999, p.363). Joblessness was a more evident issue in the New South than it had been in the old South. Joblessness and low paid work in a nation with no open welfare arrangement was a difficult issue, particularly for blacks that were oppressed and couldn’t bear the cost of the fundamental necessities of life (Hobsbawm, 1987, p.103). Managers and estate proprietors in the New South all in all would in general keep the connection between poor blacks and poor whites as disagreeable as could be expected under the circumstances. Processing plant and manor proprietors expected that that if highly contrasting laborers had a decent relationship they would shape successful worker’s guild developments and undermine the benefits of the proprietors (Lewis, 1994). Segregation for white specialists distanced blacks from them, while proprietors and managers kept control of their laborers by taking steps to utilize dark laborers as strike breakers. Such strategies were viable at keeping the development of worker’s organizations however did nothing to improve race relations in the New South (Brogan, 1999, p. 371). The formation of Birmingham, Alabama was an image of every one of that was new in the New South. The spot had not existed before 1871, and calling it Birmingham after a standout amongst the most industrialized urban communities in Britain was an announcement of purpose. Birmingham, Alabama was to be the mechanical heart of the N

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