# Linear Programming: Toy Store

In the beginning we were given a linear programming project to do for math class. Linear programming is a method to achieve the best outcome in a mathematical model. We were given an assignment in which we are the owners of a toy store and have 5 different types of toys that we make. The objective of the project is that we need to find out which 2 toy combination will make us the most profit.

First we found out that there were 10 different combinations that we could have for the project, because there could not be permutations in the toys. Next we calculated Dolls and Rocking Horses and to start things off, made 5 inequalities. Next we put these equations in slope- intercept form and then graphed them. Then

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We made 5 inequalities because both of them needed all the materials. Then we put them in slope intercept form and the graphed them to find the feasible region. We put them in standard for the purpose of this graph. Then we made 2 by 2 systems of equation to find the common points. Finally we plugged the point in our maximum profit equation ($19.55x+43.35y=p) to find the answer $3746.80.

Tinker Toys and Bears:

Purple Line and Orange Line

Finally we did hammocks and bears. We made all 5 inequalities and a profit equation. Then we put the inequalities in slope intercept form to find the feasible region but for the purpose of this paper put them in standard form. Then we did a 2 by 2 system of equations to find the common points. After that we put it in our profit equation($43.35x+$22.10y) and got $4144.60

Hammocks and Bears:

Blue Line and Orange Line

Green Line and Orange Line

In conclusion, rocking horses and hammocks are the best combination. If you make 76 rocking horses ($37.4) and 46 hammocks ($43.35), then you will have a profit of $4836.5. Although, if you do not have much wood and more fabric, you should make 38 hammocks ($43.35) and 113 bears ($22.1), which gets you $4144.6. Overall, the most money you can make is $4836.5, but if you have a shortage of wood, you can still make