QUESTION 1

Suppose you own a campsite in Chamarel, and you wish to increase the site in order to increase your profits. You have three options- build a swimming pool and charge campers for its use build a tennis court and charge the campers for its use, or build a restaurant to supply the campers with simple hot meals. You have enough funds to undertake just one of the three options and your decision will depend on the profitability of the options.

You understand that the profitability will depend upon the weather conditions. Assume you examine the Chamarel weather records over the last 40 years and find out that on 10 occasions the summer was cool, on 20 occasion’s summer was average and on 10 occasions the summer was hot. Armed with these beliefs, you approximate the annual profitability of each course of action as follows (all figures in thousands Rs)

Table 1: Annual Profit (in thousands Rs)

                                 Cool         Average    Hot

Swimming pool             50               100          150

Tennis Court                 30              180          90

Restaurant                   170            100           40

 Probability                   a                  b             c

(a)  Find out optimal decision using the 

(i)  maximax criterion,

(ii)  maximin criterion,

(iii)  You are a realist and believe that the correct decision technique to determine best alternative is to use a coefficient of realism of 0.60, calculate your criterion of realism.  

(b)  Establish the values of a, b, and c.                         

(c)  Which plan should be selected if you use the expected monetary value criterion?                           

 (d)  Compute the expected opportunity loss for each decision, and hence determine the optimal decision.           

 (e)  How much would you be willing to give to acquire additional information about the weather?                         

QUESTION 2

Emerald Flight Catering (EFC) provides in-flight catering and support services for a number of airlines at Durban airport, serving five local South African destinations. Emerald Food Ltd is a subsidiary of EFC and has the capacity of producing daily meals but is restricted with only 45 labour-hours. The company produces vegetarian and non-vegetarian meals and details of the product mix are shown in Table 2. Each Vegetarian meal requires 5 labour-hours and non vegetarian meal requires 3 labour-hours. The company has a `daily capacity of producing 2400 sandwiches and 1800 salad dishes. It has been estimated that each vegetarian meal will generate a profit of $1.75 and $4.25 for the other meal. 

                               Sandwiches (units)   Salads (units)

 Vegetarian Meal                 200                   90

  Non vegetarian Meal          200                 180

(a)  Prepare the LP model for this problem.                   

(b)  Using graphical method, determine the best combination of meals that will make the highest income.