Linnear Programming- Picturing Cookies part 1 and part 2

There are two typed of cookies to work with: plain and icing. The Woo's want to make the highest amount of profit possible with their bakery regarding plain and iced cookies. The Woos have several constraints. The only have 110 pounds of cookie dough and they only have 32 pounds of icing. They also only have enough room to only bake 140 dozen cookies total. The also only have 15 hours to prepare the cookies. The constraints can be represented as follows:

(x represents the number of plain cookies while y represents the number of iced cookies)
Dough: (1)x + (0.7)y is less than or equal to 110 pounds (Plain cookies need 1 pound of dough while cookies with icing only requires 0.7 pounds of dough)
Icing: (0)x + (0.4)y is less than or equal to 32 pounds of icing. (The plain cookies do not require any icing, which is why they are represented with a constant of 0.)
Time: (.1)x + (.15)y is less than or equal to 15 total hours.
Oven: x+y is less than or equal to 140 total dozen cookies

The key part to this problem is the profit and cost of each cookie. Plain cookies are sold for 6$ a dozen while iced cookies are sold for 7$. It costs 4.50$ per dozen of plain cookies. It costs 5.00$ per dozen to make iced cookies.

After using these constraints, I simply used the guess and check method to find the amount of plain and iced cookies that satisfies all of the constraints while yielding the highest amount of profit. I actually created a chart to demonstrate the possible combinations of iced and plain cookies and the profit that they will result:


PLAIN
30
110
50
0
75

ICED
80
0
30
80
50

PROFIT
205$
165$
180$
160$
212.50$

Using Desmos, you can see the graphs of the different constraints and how they form a feasible region:



Below are pictures of my work