operation research

Exercices A cargo plane has three compartments for storing cargo: front, centre and rear. These compartments have the following limits on both weight and space: Compartment Weight capacity (tonnes) Space capacity (cubic metres) Front 10 6800 Centre 16 8700 Rear 8 5300 Furthermore, the weight of the cargo in the respective compartments must be the same proportion of that compartment's weight capacity to maintain the balance of the plane. The following four cargoes are available for shipment on the next flight: Cargo Weight (tonnes) Volume (cubicmetres/tonne) Profit (/tonne) ci 18 480 310 650 380 C3 23 580 350 C4 12 390 285 Any proportion of these cargoes can be accepted. The objective is to determine how much (if any) of each cargo ci, C2, C3 and C4 should be accepted and how to distribute each among the compartments so that the total profit for the flight is maximised. Formulate the above problem as a linear program 15 Exercise 2 We need to found the optimal solution of this problem with Excel solver. 2020 1 2 4 Machine Table Chair MI 14 8 M2 10 10 Total of 400 hours are available on machine M1 and 800 hours an M2. Contribution from the sale of chairsid 60 SR and from tables is 40 SR. Determine the optimal mix of tables and chairs so as to maximise the 5 6 7 Chairs Total Max Capacity Tables Decision variable Contribution 9 10 12 Machine MI Machine M2 13 14 15 -Complete the six following cells C9, D9, C12, D12, F12,C13, D13, F13. - Write the formulas of the following cells: E9=..... E12= E13=