QUESTION $2$

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

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.

$2\mathrm{.}2.$ Using a range of production output of $0-200000$ units at intervals of $5000$ units, plot the total production cost curves

of the three locations on the same graph.

$2\mathrm{.}3.$ Formulate the profit functions for each of the three locations.

$2\mathrm{.}4.$ 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?