QUESTION $2(25$ marks$)$

Horizon Manufacturers Ltd$.("$Horizon Manufacturers"$)$ is an energy resources sup$-$plier. The entity produces diesel, jet oil, and petroleum.

Extraction of crude oil

Horizon Manufacturers own crude oil fields where labourers drill holes into the earth on designated areas. These labourers are paid R$120$ per hour. The entity ensures that there are constantly enough drilling labourers on the premises to satisfy the annual demand. $1860$ drilling labour hours are required each week in a $50-$week operating year, to satisfy the demand.

Once the holes are bored $($drilled$),$ chemicals are added into the hole which brings the crude oil to the earth's surface so that it can be extracted. Four thousand eight hundred grams $($g$)$ of the chemicals are required per barrel of crude oil to be extracted. One barrel is equal to R$159$ per liter. The chemicals are purchased in $1-$kilogram packets which cost R$44$ each.

Engineers, who are paid a total of R$2050000$ per month, supervise and manage the whole process on the oil fields.

Boiling of crude oil

After extraction, the crude oil is boiled into a running liquid medium using boiler ma$-$chinery. The boiler machines have a size of $1\mathrm{.}5$ ton and a capacity of $26\mathrm{.}34$ barrels of crude oil each. Labourers $("$boilers$")$ who operate this machinery have an agreed wage of R$105$ per hour. Six boilers are required per boiling machine to perform one boiling session. It takes $12$ hours to perform a boiling session per machine and, consequently, a full operating workday. Horizon Manufacturers operates $360$ days annually. The same quantity of the running liquid medium is produced as crude oil inserted into the boiler. Horizon Manufacturers owns $6$ boiling machines which are all operative.

Production of energy resources

At this stage, once boiling is complete, Horizon Manufacturers has the choice to either continue with the production of each energy source or to sell the liquid crude oil to external parties at R$8$ per liter.

If opted to continue production, the running liquid medium is divided into $3$ tanks. Tank P is designated for the production of petroleum, Tank D is designated for diesel and Tank J is designated for jet fuel. $1$ Liter of running liquid is required to produce $1$ liter of an energy resource $($e$.$g$.1$ liter of liquid oil $=1$ liter of diesel$).$

Various chemicals are then added to each tank to manufacture each energy source. The chemicals and quantities differ between the different energy sources. The chem$-$icals added into Tank P cost R$425$ per barrel of liquid oil, R$311$ per barrel of liquid oil for diesel $($Tank D$),$ and R$538$ per barrel of liquid oil for jet fuel $($Tank J$).$

Once the energy sources are produced, they can be sold at the following prices

Horizon Manufacturers have sufficient tank capacity to satisfy the annual demand for each energy source. There is a sufficient supply of all chemicals required in the man$-$ufacturing process as well as employees available in the market

Required:

$2\mathrm{.}1$

Calculate how many liters of each petroleum, diesel, and jet fuel, respectively, Horizon Manufactures Ltd$.$ should produce annually.

$(16$ marks$)$

$2\mathrm{.}2$

Advise Horizon Manufacturers Ltd$.$ whether they should continue with the pro$-$duction of each energy resource or sell the crude oil to external parties after boiling it$.$ Motivate your answer with calculations.