Question

A consultant was hired to build an optimization model for a large marketing research company. The model is based on a consumer survey that was taken in which each person was asked to rank 30 new products in descending order based on their likelihood of purchasing the product. The consultant was assigned the task of building a model that selects the minimum number of products (which would then be introduced into the marketplace) such that the first, second, and third choice of every subject in the survey is included in the list of selected products. While building a model to figure out which products to introduce, the consultant’s boss walked up to her and said: “Look, if the model tells us we need to introduce more than 15 products, then add a constraint which limits the number of new products to 15 or less. It’s too expensive to introduce more than 15 new products.”

Evaluate this statement in terms of what you have learned so far about constrained optimization models.

Answer 1

Answer:-

Given That:-

A consultant was hired to build an optimization model for a large marketing research company. The model is based on a consumer survey that was taken in which each person was asked to rank 30 new products in descending order based on their likelihood of purchasing the product.

Step 1

It is given that a consultant was recruited to build an optimization model for marketing research business. Consumer survey is conducted in which each person ranks thirty new products in descending order based on their likelihood of purchasing the product. The consultant was allocated the task of building a model that selects the minimum number of products such that the 1st, 2nd, and 3rd choice of every subject in the survey is included in the list of selected products.
Step 2
The criterion to selecting the products is if the model requires that to introduce more than 15 products. and then add a restraint which limits the number of novel products to 15 or less.
Step 3
Justification:

Step 4
The purpose of the problem is to diminish the number of products desired. so that everyone's top three alternatives are included.
There are only two possible outcomes relative to the managements new restraint.

* The minimum number of products is < = 15; then there is no need for adding the new restraint

* The least number is > 15; then the new restraint makes the problem infeasible.
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