Can you answer this?

Ad-Board, Inc. handles radio and television promotional jobs and placements for a wide range of clients. The agency’s objective is to maximize the total audience exposure for its client’s products. Research indicates that each radio spot results in 1,000 exposures while each television spot contributes an independent 3,000 exposures. A radio spot costs P5,000 and a television spot costs P20,000. Clients provide Ad-Board with a maximum monthly budget of P1 million. Contracts with radio networks require a minimum of 100 spots per month. The agency employs account executives to place the spots. Past experience indicates that each radio spot takes 20 hours of executive effort and each television spot uses 40 hours. The agency’s account executives are available for 4000 hours per month. Find the number of radio and television spots that maximizes total audience exposure. Use simplex method.

[Sam Chak]

Hi @Ethyl Mae,

From what I can gather, it seems that the presence of integers and the phrase "maximizes total..." indicates that this is related to an Integer Linear Maximizing Problem (ILMP).

To facilitate a better understanding of the math problem and receive relevant guidance from interested users, could you express the following integers in the form of mathematical constraints? Additionally, providing the Simplex formula would be helpful, as it saves users from having to search for it online.

• 1,000 exposures
• 3,000 exposures
• P5,000
• P20,000
• P1 million
• 100 spots per month
• 20 hours
• 40 hours
• 4000 hours per month

Answer 1

[Rohit Kulkarni]

Hi Ethly Mae,

In my understanding you are trying to solve an optimization problem using simplex method.

While MATLAB's internal function linprog can solve optimization problem but it does not use simplex method.

Hence you can refer to the following custom implementation of simplex method in MATLAB to solve your problem:

Simplex Method: https://www.mathworks.com/matlabcentral/fileexchange/128263-simplex?s_tid=answers_rc2-1_p4_Topic

linprog: https://www.mathworks.com/help/optim/ug/linprog.html

Hope it helps!

[Sam Chak]

It is possible to set the linprog() solver to use the 'simplex' algortihm via 'optimoptions()' settings.

@Rohit Kulkarni, Can you verify this?

[Rohit Kulkarni]

Hi Sam,

I had tried to set the solver to 'simplex' using 'optimoptions()' settings, but got the following error:

[Torsten]

Ask your professor which method you are supposed to use when he/she writes "simplex method".

Maybe you were told to program the simplex method on your own ?