Question

A big petroleum company needs to organize the travel of 1600 of its employees and respective family’s members and the transportation of 90 tons of baggage from Fiji isle to Morocco. The available airplanes are of two types; 12 airplanes from type A capable to transport 200 travelers and 6 tons of baggage and 9 airplanes from type B capable to transport 100 travelers and 6 tons of baggage. The rental fees for type “A” airplane is 800000 USD and for type “B” airplane is 200000 USD.

1. What are the decision variables?

X: Quantity of airplanes from Type A

Y: Quantity of airplanes from Type B

2. What is the Objective function?

Objective function = Fees _(Min) or Cost _(Min) = 800,000 X + 200,000 Y

3. What are the constraints?

1. Travelers Constraint: 200 X + 100 Y ≥ 1,600
2. Baggage Constraint: 6 X + 6 Y ≥ 90
3. Type A: X ≤ 12
4. Type B: Y ≤ 9

4. What are the hidden variables?

X and Y ≥ 0

Or X ≥ 0 and Y ≥ 0

X and Y are integer since travelers and baggage cannot be decimals.

5. How many corners did you find in the polygon of acceptable and feasible solutions?

1. 200 X + 100 Y = 1,600            b)   6 X + 6 Y = 90                    c)   X = 12   (12, 0)        d) Y = 9   (0, 9)

X = 0, Y = 16 (0, 16)                     X = 0, Y = 15   (0, 15)

Y = 0, X = 8    (8, 0)                       Y = 0, X = 15   (15, 0)

6. What are the coordinates of each corner?

7. Analyze the situation for every corner’s solution.

8. What is the optimal solution?
9. Is there any extra opportunity in terms of management? Develop based on your findings this opportunity if any.

Answer 1