| 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. |
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| 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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