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My homework ,which related to lean production course, is posted in below link

http://www.upsieutoc.com/image/pQnDfy

Solve the following modified entropy optimization problem. For ease of solution you can solve the problem ignoring the non-negativity constraints on p and q and then verify that they are satisfied.
min p log p +2qlog q
subject to p+q = 1
p,q >=0
Consider the following problem related to entropy maximisation in information theory. For ease of solution you can solve the problem ignoring the non-negativity constraints on p and q and then verify that they are satisfied.
min p log P + q log q
subject to p+q =1
p,q.>=0
i. Solve the primal problem directly
ii. Obtain the dual problem and solve it. Verify it gives the same answer as the primal problem.
iii. By doing an internet search or looking up textbooks, explain why this problem would be
called an “entropy maximisation” problem.

Solve the following optimisation problem
min x^2 + y^2

Subject to x+2y >= 1
A piston-cylinder device contains 1.38 kg of refrigerant-134a at -10 oC. The piston that is free to move has a mass of 16 kg and a diameter of 11.18 cm. The local atmospheric pressure is 84 kPa. Now, heat is transferred to refrigerant-134a until the temperature is 90 oC. Determine (a) the final pressure (kPa), (b) the change in the volume of the cylinder (m3), and (c) the change in the enthalpy of the refrigerant-134a (kJ/g).
Submit your answer by mutiplying the answers (a)*(b)*(c) = _______.
Two couples act on the beam as shown. If the magnitude of F is 350 lb, determine the resultant
couple moment.
Consider the system
H(z)=(1-2z^(-1)+2z^(-2)-z^(-3))/((1-z^(-1))(1-0.5z^(-1))(1-0.2z^(-1))) , ROC:0.5|z|>1
Sketch the pole – zero plots. Is the system stable?
Determine the impulse response of the system.
Explain the disadvantages of operating reactor isothermally and what is the impact of this disadvantage?
For the following gates, draw its circuit symbol and its truth table.
6.1 AND gate
6.2 NAND gate
6.3 Exclusive AND gate
6.4 OR gate
6.5 NOR gate
6.6 Exclusive OR gate
6.7 NOT gate
How the degree of polynomial in continuous path is estimated with its acceleration and velocity