# Linear Programming Games

• Imma Curiel
Part of the Theory and Decision Library book series (TDLC, volume 16)

## Abstract

Three friends, Fred, Grace, and Henry, are looking into the possibilities of starting a day care center for children from (practically) 0 to 4 years. After a thorough investigation of the local regulations and market, they come to the following assessment of the situation. They need one nursemaid per four children from 0 to 2, and one nursemaid per 10 children from 2 to 4. For each child from 0 to 2 they are required to have 8 square meters available inside, and 4 outside. For a child from 2 to 4 the requirements are 5 and 6, respectively. After calculating all costs they realize that they can make a net profit of \$200 per month per child from 0 to 2 and a net profit of \$150 per month per child from 2 to 4. (The difference is due to the fact that since there are not many day care centers that accept children form 0 to 2 years they can ask a higher fee for them.) Fred knows 9 people whom he can hire as nursemaids. He has the possibility of renting 260 square meters inside and 200 outside. While considering the possibility of starting a day care center on his own he wants to calculate the maximum profit that he can make while complying with all regulations. Therefore he has to solve the following linear programming problem.1

## Keywords

Dual Problem Linear Programming Problem Core Element Simple Game Price Vector
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.