Linnear Programming- Profitable Pictures

Profitable Pictures represents another problem that incorporates linear programming. This problem only presents two constraints, as opposed to four constraints in the Cookies problem. The artist Hassan is selling pastels and watercolors. The pastels cost 5$ each to make while the watercolors cost him 15$ to make. He overall has 180$ to spend on materials. He can only make at most 16 pictures and he wants to find the best combination of pastels and watercolors to get him the most profit.
There are two constraints:

1. p+w is less than or equal to 16 (represents the number of pictures)
2. 5p + 15w is less than or equal to 180 (represents the money that he can spend on materials)

In solving this problem, I again created different combinations of pastels and watercolors that are possible and I found the resulting profit:

Pastels (y)
5
10
0
6

Watercolors (x)
8
6
10
10

Profit
1000$
1000$
1000$
1240$

After using these combinations, I felt that the highest amount of profit that Hassan can make is 1240$. It is also important to note that (10,6) is the solution to the systems of inequalities, meaning that it is the intersection of both inequalities. This represents the best combination because it is the only point that is at the highest point of the feasible region that involves both inequalities.

Using Desmos once again, you can see the constraints on the graph and the feasible region that can be used:




Below are pictures of the work that I created for this problem. It is important to note that any stars on the graph represent possible combinations:









The last picture of my work represents combinations that can be made that yield a profit of 500$ and 600$.