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Some members of the marketing department are agitating for more high roller clients because they perceive that this provides a better revenue stream. Senior management have responded by asking the Financial Controller to provide two alternative plans, in addition to the base case information outlined above.


Alternative 1: The following amendments are required:
1. The buffet dining area (currently 5,000 square feet) could be modified. If the buffet is scaled down then the buffet dining area would require only 1500 square feet and marketing don’t think that this will change the amount spent on food by the gamblers. The show dining and dance area would be left at 5,000 square feet.
2. The maximum number of players for game of chance players and high rollers should be removed.


Alternatives 2: The following amendments are required:
1. The senior management thinks it is possible to generate a daily income of more than $1,500,000.
2. Both the buffet dining area (currently 5,000 square feet) and the show dining and dance area (currently 5,000 square feet) could be modified to a reasonable size. However, the management reminds that both Games and Show guests spends substantial amount on food and drinks. Hence, too small and no dining area could potentially discourage the
gamers and show guests going to the casino.
3. The minimum and maximum number for each type of guests can be modified with the condition that management wants a good mixed of each type of guest. 

General Business Problem                    
                         
Holiday Entertainment Corporation (HEC), the company you work for has recently purchased a
hotel with a ground-floor casino. The hotel can accommodate 1,080 guests. Its large ground
floor area is going to be devoted to a casino, dining and stage shows.
The HEC Senior management wants to remodel the casino to maximise income. 
         
         
         
                         
  Base revenue per day Food and drink revenue per day Expense Per Day Minimum Each day Maximum each day Square feet needed  Side Effects / guest     
Type of guest    Pokies  Gamers Show Guests High Rollers    
Pokies $200 $25 $1 600 800 15 $0.00 -$0.20 -$0.08 -$0.20    
Gamers $300 $100 $40 400 800 30 $0.00 $0.00 $0.00 $0.40    
Show Guests $100 $125 $10 300 800 10 $0.00 $0.00 $0.00 $0.00    
High Rollers $5,000 $0 $500 20 60 100 $0.00 $0.50 $0.00 $0.00    
                         
           
         
                         
  Pokies Gamers Show Guests High Rollers                
Revenue per day $225.00 $400.00 $225.00 $5,000.00                
Expense Per day $1 $40 $10 $500                
Side Effects $0.00 -$90.00 -$48.00 $142.00                
Profit (=Revenue- Expense) $224.00 $360.00 $215.00 $4,500.00                
Number of guest per day 600 655 535 60                
Total Profit ######                      
  P G S H                
Formulating the Problem                    
                         
The decision variables in this investment planning problems correspond to the amount that should be supplied in each material. In this situtation, to model the maximize profit decision as an linear programming problem, we let:          
         
                         
                         
  P  = the number of Pokies guest                     
  G  = the number of Gamers                     
  S  = the number of Show guests                     
  H  = the number of High Rollers                     
                         
Maximize amount of profit                         
                         
    =(Revenue-Expense)+ Side effects                    
    =224*P+360*G+215*S+4500*H+(-0.2*P+0.5*H-0.08*P-0.2*P+0.4*G)                    
                         
                         
The constraints control the quantity that may be supplied for each product                        
                         
    600 <= P <= 800                    
    400 <= G <= 800                     
    300 <= S <= 800                    
    20 <= H <= 60                    
    15*P+30*G+10*S+100*H <= 40,000                    
    P+G+S+H <= 1,850                    
                         
    P, G, S, H >= 0 (Non negetivity)                    
                         
                         
                         
This report intends to provide an insight towards the management of Holiday Entertainment Corporation (HEC). As per the given information, the analyst has developed one base case and two alternative cases to quantifying the financial impacts of different alternatives. The excel model attached here with supports the evaluation of all three options and helped to draw conclusion regarding the best choice.          
         
         
         
                         
  Pokies Gamers Show Guests High Rollers                
Solution value 600 655 535 60                
Revenue per day $225 $400 $225 $5,000 $8,17,375.00              
Expense Per day $1 $40 $10 $500 $62,150.00              
Total Side Effects $0 -$90 -$48 $142 -$76,110.00       First of all, if the base case is taken into consideration, then it can be said that the corporation can attain a profit figure of $6,79,115.00 with following all the given conditions. Not only has that the sensitivity report associated with this base case also indicates that even if the number of guests reduced by 157, then also the corporation will evidence same level of profit.  
Profit $224 $270 $167 $4,642 $6,79,115.00        
Constraints                  
Total Guest 1 1 1 1 1850 <= 1850    
Total Space 15 30 10 100 40000 <= 40000    
Guest type 1 0 0 0 600 <= 800    
Guest type 0 1 0 0 655 <= 800    
Guest type 0 0 1 0 535 <= 800    
Guest type 0 0 0 1 60 <= 60    
Guest type 1 0 0 0 600 >= 600    
Guest type 0 1 0 0 655 >= 400    
Guest type 0 0 1 0 535 >= 300          
Guest type 0 0 0 1 60 >= 20          
                         
                         
                         
                         
                         
                         
Engine: GRG Nonlinear                    
Solution Time: 0.016 Seconds.                    
Iterations: 0 Subproblems: 0                    
                         
Max Time 100 sec,  Iterations 100, Precision 0.000001                    
 Convergence 0.0001, Population Size 100, Random Seed 0, Derivatives Forward, Require Bounds                  
Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 5%, Solve Without Integer Constraints, Assume NonNegative            
                         
                         
Cell Name Original Value Final Value                  
$F$8 Profit $0.00 $6,79,115.00                  
                         
                         
                         
Cell Name Original Value Final Value Integer                
$B$4 Solution value Pokies 0 600 Contin                
$C$4 Solution value Gamers 0 655 Contin                
$D$4 Solution value Show Guests 0 535 Contin                
$E$4 Solution value High Rollers 0 60 Contin                
                         
                         
                         
Cell Name Cell Value Formula Status Slack              
$F$10 Total Guest 1850 $F$10<=$H$10 Binding 0              
$F$11 Total Space 40000 $F$11<=$H$11 Binding 0              
$F$12 Guest type 600 $F$12<=$H$12 Not Binding 200              
$F$13 Guest type 655 $F$13<=$H$13 Not Binding 145              
$F$14 Guest type 535 $F$14<=$H$14 Not Binding 265              
$F$15 Guest type 60 $F$15<=$H$15 Binding 0              
$F$16 Guest type 600 $F$16>=$H$16 Binding 0              
$F$17 Guest type 655 $F$17>=$H$17 Not Binding 255              
$F$18 Guest type 535 $F$18>=$H$18 Not Binding 235              
$F$19 Guest type 60 $F$19>=$H$19 Not Binding 40              
                         
                         
    Final Reduced                  
Cell Name Value Gradient                  
$B$4 Solution value Pokies 600 0                  
$C$4 Solution value Gamers 655 0                  
$D$4 Solution value Show Guests 535 0                  
$E$4 Solution value High Rollers 60 0                  
                         
                         
    Final Lagrange                  
Cell Name Value Multiplier                  
$F$10 Total Guest 1850 103.5                  
$F$11 Total Space 40000 6.35                  
$F$12 Guest type 600 0                  
$F$13 Guest type 655 0                  
$F$14 Guest type 535 0                  
$F$15 Guest type 60 4231                  
$F$16 Guest type 600 -160.5499992                  
$F$17 Guest type 655 0                  
$F$18 Guest type 535 0                  
$F$19 Guest type 60 0                  
                         
                  Now, as the corporation wanted further evaluation considering two alternatives, the analyst has performed the same. In alternative 1, it was mentioned that the dining area can be reduced to 1500 sq ft and the upper limit of number of gamers and high rollers needs to be removed. If the corporation does the same, then this base model will give a different profit figure of $12,20,369.50. Clearly, the profit figure will increase to a significant level as the total space now be utilised by 3500 sq ft extra. In addition, the total number of high rollers will also increase, which means, there will be more amount of direct revenue and less amount of side effects.
 
In this case, the sensitivity report indicates that even though the total number of guests will be lower than the base case, the corporation will evidence superior profits mainly because the guest type. Here also, even if the total of guest reduced from this predicted figure by 355, then also the same level of revenue will be there. Hence, even if the expense will increase to a significant level, alternative option 1 will be considered as more beneficial than base case.
 
  Pokies Gamers Show Guests High Rollers          
Solution value 600 400 300 195          
Revenue per day $225 $400 $225 $5,000 $13,37,500.00        
Expense Per day $1 $40 $10 $500 $1,17,100.00        
Total Side Effects $0 -$23 -$48 $40 -$15,600.00        
Profit $224 $338 $167 $4,540 $12,04,800.00        
Constraints                  
Total Guest 1 1 1 1 1495 <= 1850    
Total Space 15 30 10 100 43500 <= 43500    
Maximum Pokies 1 0 0 0 600 <= 800    
Guest type 0 0 1 0 300 <= 800    
Guest type 1 0 0 0 600 >= 600    
Guest type 0 1 0 0 400 >= 400    
Guest type 0 0 1 0 300 >= 300    
Guest type 0 0 0 1 195 >= 20    
                   
                   
                   
                   
                   
                         
                         
                         
                         
Engine: GRG Nonlinear                    
Solution Time: 0.063 Seconds.                    
Iterations: 7 Subproblems: 0                    
                         
Max Time 100 sec,  Iterations 100, Precision 0.000001                    
 Convergence 0.0001, Population Size 100, Random Seed 0, Derivatives Forward, Require Bounds                  
Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 5%, Solve Without Integer Constraints, Assume NonNegative            
                         
                         
Cell Name Original Value Final Value                  
$F$8 Profit $0.00 $12,04,800.00                  
                         
                         
                         
Cell Name Original Value Final Value Integer                
$B$4 Solution value Pokies 0 600 Contin                
$C$4 Solution value Gamers 0 400 Contin                
$D$4 Solution value Show Guests 0 300 Contin                
$E$4 Solution value High Rollers 0 195 Contin                
                         
                         
                         
Cell Name Cell Value Formula Status Slack              
$F$10 Total Guest 1495 $F$10<=$H$10 Not Binding 355              
$F$11 Total Space 43500 $F$11<=$H$11 Binding 0              
$F$12 Guest type 600 $F$12<=$H$12 Not Binding 200              
$F$13 Guest type 300 $F$13<=$H$13 Not Binding 500              
$F$14 Guest type 600 $F$14>=$H$14 Binding 0              
$F$15 Guest type 400 $F$15>=$H$15 Binding 0              
$F$16 Guest type 300 $F$16>=$H$16 Binding 0              
$F$17 Guest type 195 $F$17>=$H$17 Not Binding 175              
                         
                         
    Final Reduced                  
Cell Name Value Gradient                  
$B$4 Solution value Pokies 600 0                  
$C$4 Solution value Gamers 400 0                  
$D$4 Solution value Show Guests 300 0                  
$E$4 Solution value High Rollers 195 0                  
                         
                         
    Final Lagrange                  
Cell Name Value Multiplier                  
$F$10 Total Guest 1495 0                  
$F$11 Total Space 43500 47.4                  
$F$12 Guest type 600 0                  
$F$13 Guest type 300 0                  
$F$14 Guest type 600 -630                  
$F$15 Guest type 400 -1006.5                  
$F$16 Guest type 300 -307                  
$F$17 Guest type 195 0                  
                         
                         
  Pokies Gamers Show Guests High Rollers      Pokies  Gamers Show Guests High Rollers    
Solution value 64 131 43 461     0 1 0 1    
Revenue per day $225 $400 $225 $5,000 $23,80,038.93              
Expense Per day $1 $40 $10 $500 $2,36,088.06              
Total Side Effects $0 $230 $0 $52 $54,314.03         Now, if the second alternative is taken into consideration then it can be seen that the management of Holiday Entertainment Corporation (HEC) wanted to get a profit figure more than $15,00,000.00. For that they are ready to reduce the show area as well as dining area to a significant level and also want a mixed type of guest of at least two types. Considering those changes the analyst has built another alternative model.
As per this new model, the management of Holiday Entertainment Corporation (HEC) can earn a profit of $21,48,172.98. However, this can be achieved only though accessing the maximum space available for casino. This will not be a feasible solution as in such case there will not be any space for buffet dining and dance area. Hence, even if alternative 2 is giving the management the desired level of profit, it may not a choice for them.
Thus, to conclude it can be said that alternative 1 will be the best choice for Holiday Entertainment Corporation (HEC).  
Profit $224 $590 $215 $4,552 $21,98,264.91        
Constraints                  
Total Guest 0 1 0 1 592 <= 1850    
Total Space Minimum 0 30 0 100 50000 >= 40000    
Total Space Maximum 0 30 0 100 50000 <= 50000    
Guest type 0 1 0 1 2 >= 2    
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                         
Result: Solver cannot improve the current solution.  All Constraints are satisfied.                    
Solver Engine                      
  Engine: GRG Nonlinear                    
  Solution Time: 0.094 Seconds.                    
  Iterations: 8 Subproblems: 0                    
Solver Options                      
  Max Time 100 sec,  Iterations 100, Precision 0.0000001                    
   Convergence 0.0001, Population Size 100, Random Seed 0, Derivatives Forward, Require Bounds                
  Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 5%, Solve Without Integer Constraints, Assume NonNegative          
                         
Objective Cell (Max)                    
  Cell Name Original Value Final Value                
  $F$8 Profit $0.00 $21,98,264.91                
                         
                         
Variable Cells                      
  Cell Name Original Value Final Value Integer              
  $B$4 Solution value Pokies 0 64 Integer              
  $C$4 Solution value Gamers 0 131 Integer              
  $D$4 Solution value Show Guests 0 43 Integer              
  $E$4 Solution value High Rollers 0 461 Integer              
  $H$4 Solution value Pokies 0 0 Binary              
  $I$4 Solution value Gamers 0 1 Binary              
  $J$4 Solution value Show Guests 0 0 Binary              
  $K$4 Solution value High Rollers 0 1 Binary              
                         
                         
Constraints                      
  Cell Name Cell Value Formula Status Slack            
  $F$10 Total Guest 592 $F$10<=$H$10 Not Binding 1258.305            
  $F$11 Total Space Minimum 50000 $F$11>=$H$11 Not Binding 10000            
  $F$12 Total Space Maximum 50000 $F$12<=$H$12 Binding 0            
  $F$13 Guest type 2 $F$13>=$H$13 Binding 0            
  $B$4:$E$4=Integer                    
  $H$4:$K$4=Binary                    
                         
                         
Variable Cells                      
      Final Reduced                
  Cell Name Value Gradient                
  $B$4 Solution value Pokies 63.9097853 0                
  $C$4 Solution value Gamers 130.9934173 0                
  $D$4 Solution value Show Guests 43.34218135 0                
  $E$4 Solution value High Rollers 460.7019748 0                
  $H$4 Solution value Pokies 0 105280.6278                
  $I$4 Solution value Gamers 1 0                
  $J$4 Solution value Show Guests 0 137319.5847                
  $K$4 Solution value High Rollers 1 -1939963.978                
                         
Constraints                      
      Final Lagrange                
  Cell Name Value Multiplier                
  $F$10 Total Guest 591.6953921 0                
  $F$11 Total Space Minimum 50000 0                
  $F$12 Total Space Maximum 50000 46.17894043                
  $F$13 Guest type 2 -157334.5448                
                         
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