ADMS 3330 Study Guide - Feasible Region, Linear Programming, Dvd Region Code

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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

2. InvestCo is an investment firm that manages stock portfolios for a number of clients. A new client is requesting that the firm handle his funds. As an initial investment strategy, the client would like to restrict the portfolio to a mix of two stocks: Alaska Oil and Southeast Petroleum. The price of Alaska Oil is $38 per share and the price of Southeast Petroleum is $45 per share. Let x:= number of shares of Alaska Oil y:= number of shares of Southeast Petroleum

a) Write an expression for the total number of shares purchased for the client.

b) Estimated Annual Return is $9 per Alaska Oil share and $7 per Southeast Petroleum share. Develop an objective function to maximize the total annual return.

c) Total investment funds available are $83,000 for the client. Develop a constraint to model this situation.

d) Maximum Alaska Oil investment is $47,000 and maximum Southeast Petroleum investment is $42,000. Develop constraints to model this situation.

e) Of course it is not possible to purchase a negative number of shares. Develop sign restrictions to model this situation.

f) Formulate a Linear Programming model to maximize the annual return for the client (Write the complete model for the problem).

g) Is (x, y) = (1200, 900) a feasible solution for the model you formulated in part f)? Why or Why not?

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.

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 – 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 “high” impact and “low” impact ads:

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 – show all steps/calculations) and solve it using Excel’s Solver. Generate Answer report and sensitivity reports.

Use the Answer and Sensitivity reports to develop a managerial report addressing the following questions (be specific – 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.