Suppose there are two machines and three jobs. We need to complete the three jobs as soon as possible by assigning the machines to jobs in an optimal way. The following diagram depicts all possible ways of assigning machines to jobs and their respective completion times in minutes. $($Note: M stands for Machine and I stands for Job$)$

M$1$

$12$

$13$

Answer the following questions assuming that we are going to use the genetic algorithm approach to solve this problem.

a$.$ Draw a diagram to depict a suitable chromosome structure. $(4$ marks$)$

b$.$ Write down the objective function. $(3$ marks$)$

c$.$ Describe the steps in one iteration of the genetic algorithm taking the initial population size as $4.$ You are expected to be very clear on each step to obtain full marks. $(6$ marks$)$

d$.$ Suppose there is a condition that a machine can be assigned to at most two jobs. How would you handle this condition in your genetic algorithm design? $(4$ marks$)$