SO Homework May14, 2019
Exercise 1A new producer of perfume wish to get a break into a lucrative market. An
exclusive fragrance, Chinelle, is to be produced and marketed. With the equipment
available it is possible to produce the perfume using two alternative processes, and the
company also consider utilizing the services of a famous model when launching it. In
order to simplify the problem, let us assume that the perfume is manufactured by the
use of two main ingredients—the first a secret substance called MO and the second a
more well-known mixture of ingredients. The first of the two processes available
provides three grams of perfume for every unit of MO and two units of the standard
substance, while the other process gives five grams of perfume for every two
(respectively, three) units of the two main ingredients. The company has at its disposal
manufacturing processes that can produce at most 20,000 units of MO during the
planning period and 35,000 units of the standard mixture. Every unit of MO costs three
EUR (it is manufactured in France) to produce, and the other mixture only two EUR
per unit. One gram of the new perfume will cost fifty EUR. Even without any
advertising the company thinks they can sell 1000 grams of the perfume, simply
because of the news value. A famous model can be contracted for commercials, costing
5,000 EUR per photo session (which takes half an hour), and the company thinks that
a campaign using his image can raise the demand by about 200 grams per half hour of
his time, but not exceeding three hours (he has many other offers).
Formulate a mathematical model of the best production strategy problem.