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Variables and minimization objective function

a) Using your own LP model with two variables and minimisation objective function, illustrate graphically how you can find the shadow price of a binding constraint.

b) Explain how ranked goal programming works and briefly explain why this approach may be preferred over the weighted goal programming approach.

c) Why are integer linear programming models (as compared with standard linear programming models) in general more difficult to solve?

d) Explain what is meant by the reduced cost of a decision variable and briefly comment why this information may be of interest to a decision maker.

e) What is the difference between decision making under certainty, decision making under risk and decision making under uncertainty?

f) Describe two applications of the shortest path problem.

g) A box contains 8 red balls, 10 green balls and 2 white balls. A ball is removed from the box and replaced; the balls are mixed and then another ball is removed. What is the probability of:

  1. two green balls being drawn?
  2. a red ball on the second draw?
  3. A red or white ball on the first draw, and a green or white ball on the second draw?
  4. a red ball on the second draw, given that a white ball was drawn on the first?
  5. Re-examine part (1) in case the first ball is not replaced in the box.

h) Nottingham University must purchase 1100 computers from three potential suppliers. Supplier 1 charges £500 per computer plus a (fixed) delivery charge of
£5000. Supplier 2 charges £350 per computer plus a (fixed) delivery charge of
£4000. Supplier 3 charges £250 per computer plus a (fixed) delivery charge of
£6000. Supplier 1 will sell at most 500 computers; supplier 2, at most 900; and supplier 3, at most 400. Formulate an integer linear programming model to minimise the cost of purchasing the needed computers. Clearly define the decision variables and explain the objective function and constraints.

Sample Solution

Thirdly, the characters involved are a key feature to any story. “In order to get personally involved with a story, we, as readers or listeners, must be able to identify with the characters” (Fog, 2004:41). The use of characters helps to create the emotional connection to the consumer as spoken about previously. The way it does this is because as a consumer, we may be able to see part of our self in one of the characters. This makes a relation between the consumer and the character. The reason for this is because if we can identify with the characters, we can fully embrace and understand the story. The last point is the plot is something that is divided into three parts, the beginning, middle and end. At the very beginning of the story, the scene is set and “the progression of change creates conflict and sets the parameters for the rest of the story. The conflict escalates but is finally resolved, marking the end of the story” (Fog, 2004:44). The reason the plot and flow of the story is so important, is because “it is vital to the consumer’s experience” (Fog, 2004:44). The plot is something that can be developed over time to create a more immersive experience, or can be done cleverly in 30 second advertisements to catch the consumers attention. Now the four ‘checkpoints’ have been outlined and explained, it’s time to work out how brands apply this to their marketing and advertisement strategies. Once it is understood how these brands apply storytelling, it will become visible how they can “create identification, engagement and relevance” (Fog, 2004:164) with their consumers. Brands use storytelling as a sales promotion tool, and “More and more companies are looking to create a story universe surrounding their products and services. In doing so, their story becomes the driving force behind their brand values” (Fog, 2004:164). When companies can tell an immersive story through their marketing and advertisements over a long period, Klaus Fog refers to brands being able to create a “story universe surrounding their products and services” (Fog, 2004:164). The fact that Fog identifies the stories that brands tell as a fictional universe, allows the consumer to get fully immersed in the story. This is where the story becomes “the driving force behind their brand values” (Fog, 2004:164). By creating this other ‘universe’ revolved completely around the brand, they can strengthen their image, and make an even stronger emotional connection to the consumer, which separates them from other brands. Storytelling can be applied to many different marketing techniques, including adver

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