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? $(1$ marks$)$ This module is operations management in supply chain