A company is planning next month's production. It has to pay a setup cost to produce a batch of X$4\text{'}$s so if it does produce a batch it wants to produce at least $100$ units. Which of the following pairs of constraints show the relationship$($s$)$ between the setup variable $4$ and the production quantity variable X$4?$

a$.$ X$4<=$ M$44,$ X$4>=100$

b$.$ X$4<=$ M$4$Y$4,$ X$4>=100$ Y$4$

c$.$ X$4<=$ M$474,$ X$4<=100$ Y$4$

d$.$ X$4<=$ M$44,$ X$4=100$ Y$4$