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Consider the Linear Programme (LP)
Max 4x + 6y
subject to 3x + 2y ≤ 6, 2x +3y ≤ 6, x, y ≥ 0
[1] After introducing slack variables s and t, the initial basic feasible solution is represented by the table below (basic variables are s = 6 and t = 6, and the objective function value is 0). -4 -6 0 0 0 s 3 2 1 0 6 t 2 3 0 1 6 x y s t RHS
After some simplex iterations, the following table is obtained0 0 0 2 12 s 5/3 0 1 -1/3 2 y 2/3 1 0 1/3 2 x y s t RHS
From this, one can conclude that [2 marks]
(A) the LP has a unique optimal solution
(B) the LP has an optimal solution that is not unique
(C) the LP is infeasible
(D) the LP is unbounded
[2] The dual for the LP in the above question is [2 marks]
(A) Min 6u + 6v
subject to 3u + 2v ≥ 4, 2u + 3v ≥ 6, u, v ≥ 0
(B) Max 6u + 6v
subject to 3u + 2v ≤ 4, 2u + 3v ≥ 6, u, v ≥ 0
(C) Max 4u + 6v
subject to 3u + 2v ≥ 6, 2u + 3v ≥ 6, u, v ≥ 0
(D) Min 4u + 6v
subject to 3u + 2v ≤ 6, 2u + 3v ≥ 6, u, v ≥ 0asked in Mechanical Engineering, 2008
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8.
In the figure shown, the system is a pure substance kept in a piston- cylinder arrangement. The system is initially a two-phase mixture containing 1 kg of liquid and 0.03 kg of vapour at a pressure of 100 kPa. Initially, the piston rests on a set of stops, as shown in the figure. A pressure of 200kPa is required to exactly balance the weight of the piston and the outside atmospheric pressure. Heat transfer takes place into the system until its volume increases by 50%. Heat transfer to the system occurs in such a manner that the piston, when allowed to move, does so in a very slow (quasi – static / quasi – equilibrium) process. The thermal reservoir from which heat is transferred to the system has a temperature of 400°C. Average temperature of the system boundary can be taken as 175°C. The heat transfer to the system is 1kJ, during which its entropy increase by 10 J/K.
Specific volume of liquid (vf) and vapour (vg) phases, as well as values of saturation temperatures, are given in the below.
Pressure (kPa)
Saturation Temperature, Tsat (°C)
Vf (m3/kg)
Vg (m3/kg)
100
100
0.001
0.1
200
200
0.0015
0.002
[1] At the end of the process, which one of the following situations will be true? [2 marks]
(A) superheated vapour will be left in the system
(B) no vapour will be left in the system
(C) a liquid + vapour mixture will be left in the system
(D) the mixture will exist at a dry saturate vapour state[2] The work done by the system during the process is [2 marks]
(A) 0.1 kJ
(B) 0.2 kJ
(C) 0.3 kJ
(D) 0.4 kJ[3] The net entropy generation (considering the system and the thermal reservoir together) during the process is closest to [2 marks]
(A) 7.5 J/K
(B) 7.7 J/K
(C) 8.5 J/K
(D) 10 J/Kasked in Mechanical Engineering, 2008
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