ADMS 3330 : 3330_Ch08.doc
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1. The following is a linear programming formulation of a labor planning problem. There are four overlapping shifts, and management must decide how many employees to schedule to start work on each shift. The objective is to minimize the total number of employees required while the constraints stipulate how many employees are required at each time of day. The variables X1 - X4 represent the number of employees starting work on each shift (shift 1 through shift 4).
Minimize X1 + X2 + X3 + X4
Subject to: X1 + X4%u2265 12 (shift 1)
X1 + X2%u2265 15 (shift 2)
X2 + X3%u2265 16 (shift 3)
X3 + X4%u2265 14 (shift 4)
all variables %u2265 0
Find the optimal solution using QM.
How many workers would be assigned to shift 1? (Points : 3) 12
13
0
none of the above
moving the isoprofit lines towards the origin in a parallel fashion until the last point in the feasible region is encountered. locating the point that is highest on the graph. none of the above. all of the above. |
equal to linear to parallel to |
maximize ingredient blends. minimize production losses. maximize the number of products to be produced. minimize the costs of nutrient blends. |
different product mix, same total profit as before. same product mix, same total profit. different product mix, different total profit. |
requires that the profit from all corners of the feasible region be compared. will provide one, and only one, optimum. requires that all corners created by all constraints be compared. will not provide a solution at an intersection or corner where a non-negativity constraint is involved. |
1200 360 none of the above |
putting in a value for the objective function. choosing the options for assuming both a linear model and non-negative variables. resetting the parameters. none of the above. |
(20,50) (60,30) none of the above |
| 10. ____________ is used to analyze changes in model parameters. (Points : 3) |
Feasible solution
Sensitivity analysis
None of the above
Langoustine Restaurant LP Case
The Langoustine is an upscale seafood restaurant located in downtown Seattle, Washington. The restaurant has recently signed a contract with a new highly acclaimed chef and expanded the seating area. In preparation for the coming summer season, the principal owners of the restaurant approved an advertising budget of $279,000 and hired a local advertising firm, ACA Consulting to launch a major advertising campaign.
The ACA consultants provided the management of the restaurant with the following information about the industry exposure effectiveness per ad, their estimate of the number of potential new customers reached per ad, the cost of each ad.
| Television | Radio | Newspaper | |
| EXPOSURE | 85 | 25 | 12 |
| NEW CUSTOMERS REACHED per advertisement | 4,000 | 2,000 | 1,000 |
| COST per advertisement | $10,000 | $3,000 | $1,000 |
The exposure rating is viewed as a measure of the value of the ad to both existing and potential new customers. It is a function of such things as image, message recall, visual and audio appeal, and so on.
At this points, the ACA consultants pointed out that the data concerning exposure rating and new customer reach were only applicable to the first few ads in each medium.
For television, ACA stated that the exposure rating of 85 and 4,000 new customers reached per ad were reliable for the first 10 television ads. After 10 ads, the benefit is expected to decline â the exposure rating from additional television ads declines to 55 and the number of new customers reached goes down to 1500.
For radio ads, the preceding data are reliable up to a maximum of 15 ads. Beyond 15 ads, the exposure rating declines to 18 and the number of new customers reached declines to 1200.
Similarly, for newspaper ads, the exposure rating beyond 20 ads declines to 5 and the number of new customers reached declines to 700.
The table below summarizes the relevant data to account for the âhighâ impact and âlowâ impact ads:
| first 10 TV ads | additional TV ads beyond 10 | First 15 | additional radio ads | first 20 | additional newspaper ads | |
| EXPOSURE | 85 | 55 | 25 | 18 | 12 | 5 |
| NEW CUSTOMERS | 4,000 | 1,500 | 2,000 | 1,200 | 1,000 | 700 |
| COST per | $10,000 | $10,000 | $3,000 | $3,000 | $1,000 | $1,000 |
Assume that the management of the Langoustine accepted maximizing the total number of new customers reached, across all media, as the objective of the advertising campaign. In addition, the following guidelines were adopted:
Use no more than 20 television ads
Allocate at least 140,000 dollars to the television ads
Restrict the radio advertising budget to $90,000 (allocate no more than $90,000 to radio ads)
Allocate at least $30,000 to newspaper budget
Use at least twice as many radio advertisements as television advertisements.
Set the minimum on the total exposure rating from the advertising campaign to 2,000
How many television, radio and newspaper advertisements should be used to maximize number of potential customers reached and meet all of the guidelines and the budget constraint of $279,000
Formulate a linear programming model for this media selection problem (define decision variables, write down the objective function, develop constraints â show all steps/calculations) and solve it using Excelâs Solver. Generate Answer report and sensitivity reports.
Use the Answer and Sensitivity reports to develop a managerial report addressing the following questions (be specific â justify your answers by referring to reduced cost, or range of optimality, or shadow price etc.):
1.How many advertisement for television, radio and newspapers should be used to maximize the number of potential customers reached by the campaign? How will the advertising budget be allocated to each type of media?
2.What will be the total exposure rating of the ad campaign?
3.Would you recommend increasing the current $140,000 limit on advertising budget for television advertisements to 141,000 dollars? Explain/justify your answer.
4.If the current advertising budget of 279,000 was reduced by $1,000 what would be the total number of potential new customers reached?
5.If the estimate of the number of potential new customers reached by the first 15 television ads were revised by ACA downward to 3000 (from 4000), would the budget allocation change? Explain/Justify.
Capital Budgeting Case Study
Instructions: The assignment is based onthe case below. The instruction relating to the assignment is atthe end of the case.
Dan and Susan are facing an important decision. After havingdiscussed different financial scenarios, the two computer engineersfelt it was time to finalize their cash flow projections and moveto the next stage â decide which of two possible projects theyshould undertake.
Both had a bachelor degree in engineering and had put in severalyears as maintenance engineers in a large chip manufacturingcompany. About six months ago, they were able to exercise theirfirst stock options. That was when they decided to quit their safe,steady job and pursue their dreams of starting a venture of theirown. In their spare time, almost as a hobby, they had beencollaborating on some research into a new chip that could speed upcertain specialized tasks by as much as 25%. At this point, thedesign of the chip was complete. While further experimentationmight improve the performance of their design, any delay inentering the market now may prove to be costly, as one of theestablished players might introduce a similar product of their own.The duo knew that now was the time to act if at all.
They estimated that they would need to spend about $1,000,000 onplant, equipment and supplies. As for future cash flows, they feltthat the right strategy at least for the first year would be tosell their product at dirt-cheap prices in order to induce customeracceptance. Then, once the product had established a name foritself, the price could be raised. By the end of the fifth year,their product in its current form was likely to be obsolete.However, the innovative approach that they had devised and patentedcould be sold to a larger chip manufacturer for a decent sum.Accordingly, the two budding entrepreneurs estimated the cash flowsfor this project (call it Project A) as follows:
Year | Project A Expected Cash flows ($) |
0 | (1,000,000) |
1 | 50,000 |
2 | 200,000 |
3 | 600,000 |
4 | 1,000,000 |
5 | 1,500,000 |
An alternative to pursuing this project would be to immediatelysell the patent for their innovative chip design to one of theestablished chip makers. They estimated that they would receivearound $200,000 for this. It would probably not be reasonable toexpect much more as neither their product nor their innovativeapproach had a track record.
They could then invest in some plant and equipment that wouldtest silicon wafers for zircon content before the wafers were usedto make chips. Too much zircon would affect the long-termperformance of the chips. The task of checking the level of zirconwas currently being performed by chip makers themselves. However,many of them, especially the smaller ones, did not have thecapacity to permit 100% checking. Most tested only a sample of thewafers they received.
Dan and Susan were confident that they could persuade at leastsome of the chip makers to outsource this function to them. Byexclusively specializing in this task, their little company wouldbe able to slash costs by more than half, and thus allow the chipmanufacturers to go in for 100% quality check for roughly the samecost as what they were incurring for a partial quality check today.The life of this project too (call it project B) is expected to beonly about five years.
The initial investment for this project is estimated at $1,100,000. After taking into account the sale of their patent, thenet investment would be $900,000. As for the future, Dan and Susanwere pretty sure that there would be sizable profits in the firstcouple of years. But thereafter, the zircon content problem wouldslowly start to disappear with advancing technology in the waferindustry. Keeping all this in mind, they estimate the cash flowsfor this project as follows:
Year | Project B Expected Cash flows ($) |
0 | ($900,000) |
1 | 650,000 |
2 | 650,000 |
3 | 550,000 |
4 | 300,000 |
5 | 100,000 |
Dan and Susan now need to make their decision. For purposes ofanalysis, they plan to use a required rate of return of 20% forboth projects. Ideally, they would prefer that the project theychoose have a payback period of less than 3.5 years and adiscounted payback period of less than 4 years.
Assignment:
Suppose that Dan and Susan have hired you as a consultant tohelp them make the decision. Please create an official presentationto present your findings and recommendations. The questions belowshould help to guide your insight.
Briefly, summarize the key facts of the case and identify theproblem being faced by our two budding entrepreneurs. In otherwords, what is the decision that they need to make? (10 points)
An excellent presentation will demonstrate the ability toconstruct a clear and insightful problem statement whileidentifying all underlying issues.
What are some approaches that can be used to solve this problem?What are various criteria or metrics that can be used to help makethis decision?
An excellent presentation will propose solutions that aresensitive to all the identified issues.
