$4\mathrm{.}1$ Rain Group Holdings $($Pvt$)$ LTD provides internet in a small suburb in Bloemfontein. The company wishes to determine the least cost way of connecting households that have subscribed to the service provider using underground fibre optic cables. Eleven possible branches have been identified that could be used to connect these households. The cost in thousands of South African rands and the branches are summarised in the table below:

$\backslash$table$[[$Table A$,$Table B$],[$Branch$,\backslash$table$[[$Start$],[$node$]],\backslash$table$[[$End$],[$Node$]],\backslash$table$[[$Cost$],[($R$1000$s$)]],$Branch,$\backslash$table$[[$Start$],[$node$]],\backslash$table$[[$End$],[$Node$]],\backslash$table$[[$Cost$],[($R$1000$s$)]]],[$Branch $1,1,2,5,$Branch $1,1,2,5],[$Branch $2,1,3,6,$Branch $2,1,3,1],[$Branch $3,1,4,6,$Branch $3,1,4,1],[$Branch $4,1,5,5,$Branch $4,1,5,1],[$Branch $5,2,6,7,$Branch $5,2,6,7],[$Branch $6,3,7,5,$Branch $6,3,7,5],[$Branch $7,4,7,7,$Branch $7,4,7,7],[$Branch $8,5,8,4,$Branch $8,5,8,4],[$Branch $9,6,7,1,$Branch $9,6,7,1],[$Branch $10,7,9,6,$Branch $10,7,9,6],[$Branch $11,8,9,2,$Branch $11,8,9,2]]$

$4\mathrm{.}1\mathrm{.}1$ Use Table A data. When using the minimal$-$spanning tree method, and if the first node selected is node $1,$ determine the least cost way to run the cable to the households and provide the order with which the branches are selected.

$4\mathrm{.}1\mathrm{.}2$ Proceed to illustrate diagrammatically, the connections of the houses.

$4\mathrm{.}1\mathrm{.}3$ Use Table B data. When using the minimal$-$spanning tree method, and if the first node selected is node $1,$ determine the least cost way to run the cable to the households and provide the order with which the branches are selected.

$4\mathrm{.}2$ A creche in Eastern Cape Province has been recommended to provide meals for their learners. The creche has hired a specialist to formulate an appropriate meal for the learners. The specialist is of the opinion that for a proper lunch meal, the following five meal content requirements should be met:

Between $1350$ and $2250$ calories

At least $6$ milligrams of iron

No more than $75$ grams of fat

At least $39$ grams of protein

No more than $75$ grams of carbohydrates