Mr. Balk and Mr. Sullivan have created their own cookie factory. In their factory, they bake two and only two types of cookies: the Balkster and the Sullivander. The Balkster cookie requires 1 pound of cookie dough per dozen while the Sullivander requires 0.7 pounds of cookie dough per dozen along with 0.4 pounds of icing. Being math geniuses they also know that the Balkster takes 0.1 hours of preparation time while the Sullivander takes 0.15 hours. Since the cookies are a hot commodity, they know that no matter how many cookies they make, they will sell all of them.

The two men want to become rich (that's why they quit being teachers). Thus, they need to decide how many dozens of each cookie they should make for their grand opening. Their decision rests upon three limiting factors:
• The ingredients they have on hand-they have 110 pounds of cookie dough and 32 pounds of icing
• The amount of oven space available---they have room to bake a total of 140 dozen cookies for the grand opening
• The amount of preparation time available---together they have 15 hours for cookie preparation

Looking within the money, the Balkster cookies cost $4.50 a dozen, but will be sold at $6.00 a dozen. The Sullivander cost $5.00 a dozen while being sold for $7.00 a dozen.

Question: How many dozens of each kind of cookie should Mr. Balk and Mr.
Sullivan make so that their profit is as high as possible?

Please type the three limiting factors.

To maximize their profit, Mr. Balk and Mr. Sullivan should determine the number of dozens of each type of cookie to make based on the given limiting factors.

Let's start by defining some variables:
- Let x represent the number of dozens of Balkster cookies they make.
- Let y represent the number of dozens of Sullivander cookies they make.

Now let's set up the objective function, which represents the profit they will make:
- The profit from selling Balkster cookies is (6.00 - 4.50) * x, or 1.5x.
- The profit from selling Sullivander cookies is (7.00 - 5.00) * y, or 2y.
- So, the total profit will be 1.5x + 2y.

Next, we need to set up the constraints based on the limiting factors:
1. Ingredients constraint:
- Each dozen of Balkster cookies requires 1 pound of cookie dough, so the weight of cookie dough used for Balkster cookies will be x pounds.
- Each dozen of Sullivander cookies requires 0.7 pounds of cookie dough, so the weight of cookie dough used for Sullivander cookies will be 0.7y pounds.
- The total weight of cookie dough used should not exceed 110 pounds: x + 0.7y ≤ 110.
- Each dozen of Sullivander cookies also requires 0.4 pounds of icing, so the weight of icing used for Sullivander cookies will be 0.4y pounds.
- The total weight of icing used should not exceed 32 pounds: 0.4y ≤ 32.

2. Oven space constraint:
- They have room to bake a total of 140 dozen cookies, so the total number of dozens of cookies can be expressed as x + y ≤ 140.

3. Preparation time constraint:
- The preparation time for Balkster cookies is 0.1 hours per dozen, so the preparation time for Balkster cookies will be 0.1x hours.
- The preparation time for Sullivander cookies is 0.15 hours per dozen, so the preparation time for Sullivander cookies will be 0.15y hours.
- The total preparation time should not exceed 15 hours: 0.1x + 0.15y ≤ 15.

Now we can solve this problem using linear programming. We can plot the feasible region on a graph and find the corner points to check which one maximizes the objective function. However, since this is a text-based conversation, I will use linear programming software instead.

Using the given constraints, the linear programming software will optimize the objective function (1.5x + 2y) and give us the values of x and y that maximize their profit.

Please note that the actual values of x and y will depend on the given data and can be solved using linear programming methods or software.