The Naturals Cosmetics Co. is considering an Ad Campaign for their new Sulphate Free Shampoo (SFS). They
Question:
The Naturals Cosmetics Co. is considering an Ad Campaign for their new Sulphate Free Shampoo
(SFS). They are considering three TV channels for the campaign Star, Galaxy and Cosmos. The
expected exposures on the 3 channels per Rs.1000 spent are 2200, 3000 and 1800 respectively.
Creating the ads for the 3 channels costs Rs. 50,000, Rs. 75,000 and Rs. 40000, respectively. The
total budget available for the campaign after creating the 3 ads is Rs. 280,000. Management does
not want to spend more than 60% of the budget on Galaxy. At least Rs. 60,000 should be allocated
to Star and Rs. 50,000 each to Galaxy and Cosmos. Also, the amount allocated to Star should not
be more than double the amount allocated to Cosmos.
The campaign cannot be judged as successful if the total exposures are under 750,000.
Management would like to decide the best allocation of the available advertising budget to the
three TV channels in order to maximize total exposures.
(a) Formulate a linear programming model that will help the Naturals Cosmetics Co. in its
decision. Define the variables clearly and label all constraints. (5 points)
(b) Upon solving the linear programming formulation, management realizes that all the stated
conditions cannot be met simultaneously. Though the budget cannot be increased and the
minimum budget allocations for Galaxy and Cosmos are mandatory, management is willing
to relax the other conditions. They would like to achieve the following in the given order of
priority:
1. Avoid allocating to Star, more than double the amount allocated to Cosmos.
2. Avoid allocating less than Rs. 60,000 to Star.
3. Minimize the under achievement of the goal of 750,000 exposures.
4. Avoid expenditure of more than 60% of the available money on Galaxy.
State the goal programming problem that needs to be solved next. Clearly define all variables
used and label all constraints. (4 points)
Expert Answer:
