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)

(c) Management is considering the following decision alternatives: Decision 1 Decision 2 Decision 3 Funds allocated to 60 O 62 Star Funds allocated to 170 230 168 Galaxy Funds allocated to 50 50 50 Cosmos