Question $3$

A frigrance corporation mamufuctures three types of perfumes: Brut perfume, Chand

profume and Eau de Parfum. For each type of perfume, the corporatiou has the optiou

to peocess further from regular to luxury perfume.

The raw material norded to mawufacture each type of perfume ean be purchood for R$250$

por kilogram $($kg$).$

Procssing $1kg$ of raw material roquires $2$ hours of labonatory time. Each klogrian of

procrssod raw material yicks $120$ millilitre $(ml$ of Brut perfime, $90ml$ of Chanel per$-$

fume and $195ml$ of Eau de Parfum.

Since the corporation also has the option of further procrseing from regular perfume to

luxury perfume,

each millilitre of regular Brut perfume procesocd furtber requires an additional $3$

bours of laboratory time and R$15$ processing enst, and ybelds $1ml$ of luxoury Brut

perfume;

each millilitre of regular Chand perfume peocossed further requires an wdilitional $4$

bours of labocatory time and R$20$ procsssing east, abd ylelds $1m.$ of luxury Chanet

perfume; and

each millilitre of regular Ean de Parfium peoossed furtber renuires an iaditional $2$

bours of laboratory time and R$12$ proossing cost, asd yields $1ml$ of luxury Eau

de Parfum.

The selling price of wach perfume per millilitre $($mI$)$ is given in the following table:

TURN OVER

CONFIDENTIAL

Phge $7$ of $9$

DSC $2605$

May$/$June

Perfume selling price per ml

Each yoar, the corporation has between $1920$ and $9600$ hours of laboratory time wval$-$

able, and it call purchase up to $3000kg$ of raw material.

The eorporation management wants to maximise the total profit by assuming that the

cost of the labocatory hours is fixod.

$3\mathrm{.}1$ Define the decisino variables of this problem cloarly.

$3\mathrm{.}2$ Formulate all the fusctional constriaints.

$3$ Formulate the objoctive fusction that maximises the total profit.

$3\mathrm{.}4$ Doduce the L$.$P model in algehraic representation form.