$1\mathrm{.}1.$ Efficient electricity management is pivotal for achieving production targets and sustaining profitability, making it a vital component of operations management. The escalating costs of energy, coupled with stringent environmental regulations and evolving supply$-$demand dynamics, underscore the pressing need for industrial organisations to curtail energy consumption and associated expenses. To secure a competitive edge in the long term, firms must prioritise continual enhancements in electricity efficiency across their operations $($Schulze$,$ Nehler, Ottosson & Thollander, $2016).$

In light of the above, examine the existing literature to elucidate how effective electricity$/$energy management can bolster operations management. $(4$ marks$)$

$1\mathrm{.}2.$ The information provided below relates to the operations of gold mining company, Pan African Resources Plc$,$ in $2022$ and $2023.$

INFORMATION

$2023$

$2022$

Total gold production

$175\mathrm{.}209$ ounces

$205\mathrm{.}688$ ounces

Revenue

R$5701\mathrm{.}0$ million

R$5709\mathrm{.}4$ million

Labour costs

R$1070\mathrm{.}7$ million $(2469$ employees$)$

R$987\mathrm{.}5$ million $(2193$ employees$)$

Electricity consumption

R$505\mathrm{.}2$ million $(1403\mathrm{.}02$TJ$)$

R$512\mathrm{.}7$ million $(1357\mathrm{.}07$TJ$)$

Capital expenditure

R$1782\mathrm{.}2$ million

R$1031\mathrm{.}3$ million

Other inputs

R$197\mathrm{.}3$ million

R$909\mathrm{.}7$ million

$1\mathrm{.}2\mathrm{.}1.$

Determine Pan African Resources$$ gold production per employee $($i$.$e$.,$ labour productivity$)$ in $2022$ and $2023($round off answer to five decimal places$)$ and comment on the results obtained by suggesting probable causes of the change in labour productivity. $(4$ marks$)$

$1\mathrm{.}2\mathrm{.}2.$

Using the sales revenue to represent the output from the operations, determine Pan African Resources$$ multifactor productivity in $2022$ and $2023($round off answers to two decimal places$)$ and comment on the results obtained. $(7$ marks$)$

QUESTION $2[15$ Marks$]$

Study the caselet provided below and answer the following questions. The management of DGB Enterprises has narrowed down the site selection for a new manufacturing facility to three potential locations $$ A$,$ B and C$.$ The information provided below shows the annual fixed costs and variable costs per unit of the product at each of three locations.

INFORMATION

Location

Fixed costs

Variable costs per unit

A

R$3000000$

R$50$

B

R$4500000$

R$25$

C

R$6000000$

R$15$

After an extensive market survey, the operations analyst of DGB Enterprises has estimated a R$75$ target selling price for each unit of the product expected to be produced at the facility.

Required:

$2\mathrm{.}1.$

Formulate the cost functions for each of the three locations. $(3$ marks$)$

$2\mathrm{.}2.$

Using a range of production output of $0200000$ units at intervals of $5000$ units, plot the total production cost curves of the three locations on the same graph. $(5$ marks$)$

$2\mathrm{.}3.$

Formulate the profit functions for each of the three locations. $(3$ marks$)$

$2\mathrm{.}4.$

Determine the profits of the three locations for an estimated production and sales volume of $175000$ units per year. $(3$ marks$)$

$2\mathrm{.}5.$

Based on the estimated production and sales volume of $175000$ units per year, which of the three locations would you recommend for the location of the new manufacturing facility?