Consider the following LP model and it is graphical solution to answer questions from a) to g). Maximize zu 4x;+5x
Subject to:
X.55
(1)
2x+x)512
(2)
Xi+2x512
-(3)
.(4)
X1, X20
10
B
2
.
a) What is the optimal solution X1, X, and z?
b) Determine the optimality range of the objective function coefficient C.
c) Determine the feasibility range of the right-hand side for constraint 1, 2 and 3.
d) How many basic feasible solutions in this problem?
e) Is there any binding constraint(s)?
1) Dose any constraint has a slack? which one and by how much?
B) Dose any constraint has a surplus? which one and by how much?

Liquid flows at steady state at a rate of 2 lb/'s through a pump, which operates to raise the elevation of the liquid 100 ft from control volume inlet to exit. the liquid specific enthalpy at the inlet is 40.09 btu/lb and at the exit is 40.94 btub. the pump requires 3 btu/s of power to operate. if kinetic energy effects are negligible and gravitational acceleration is 32.174 tt/s, the heat transfer rate associated with this steady state process is most closely 1)-2,02 btu/s from the liquid to the surroundings 2)-3.98 btu/s from the surroundings to the liquid. 3)-4.96 btu/s from the surroundings to the liquid. 4)-1.04 btu/s from the liquid to the surroundings.