QUESTION $3(20$ Marks$)$

The Coca$-$Cola Company operates several manufacturing plants in South Africa, where it produces a wide range of beverages to meet the demands of the local market. At these manufacturing facilities, Coca$-$Cola produces various beverage products, including carbonated soft drinks, juices, bottled water, energy drinks, and sports drinks. These products are manufactured using state$-$of$-$the$-$art production technologies and adhere to stringent quality and safety standards. In one of its plants in Bloemfontein, it needs to make $100,000$ litres of grapetiser per month to meet demand. Each month contains $20$ working days, each of which allows for three $(3)8-$hour shifts. Within a close radius, the organisation operates a Coke Zero processing unit which has $100,000$ labor hours available for the quarter and currently has a labor productivity of $5$ gallons per $4,000$ hours.

Using the provided information determine the following:

$3\mathrm{.}1$ For the grapetiser processing plant, if a worker can produce $10$ litres$/$hour$,$ determine the number of workers needed on each shift. Suppose each shift has $100$ workers, what is the productivity of an individual worker? Lastly, if material costs are R$10/$litre$,$ capital costs are R$100,000$ and labor costs are R$10/$hour$,$ what is the multifactor productivity of this processing plant? $(14$ Marks$)$

$3\mathrm{.}2$ For the coke$-$zero processing unit, determine the amount of gallons that the processing plant can make this quarter. If the multi$-$factor productivity was $1$ gallon per R$25000,$ how much should the organisation spend this quarter in manufacturing Coke Zero gallons?