Four shipping containers can altogether take a maximum of $20$ tons for one shipment order. The following table provides details on the weight $($in tons$)$ and value of each container.

Container

$1$

$2$

$3$

$4$

Weight of container $($tons$)$

$5$

$6$

$9$

$7$

Value $/$ Container

$$6000$

$$5500$

$$7500$

$$6000$

a$.$ Develop a binary integer model that will determine the two containers and the quantity that should be considered for shipment using these two containers to maximize the value of the shipment.

b$.$ which container$($s$)$ would be selected.

c$.$ what is the total value for the container.