QUESTION $2[15$ Marks$]$

Study the caselet provided below and answer the following questions.

Th e man ag e men t of DGB Enterprises h as n arrow e d dow n th e site selection f or a n ew man uf actu rin g f acility to th ree

poten tial locations $$ A$,$ B an d C$.$ Th e inf ormation provided below sh ows th e annu al fixed costs an d variable costs per unit

of the product at each of three location s$.$

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 su rvey, th e operations an alyst of DGB Enterprises h as estimated a R $75$ target sellin g price for

each unit of the produ ct expected to be produ ced 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$)$

$2\mathrm{.}4.$ Determin e the profits of the three locations for an estimated production and sales volume of $175000$ units per year.