1. Baker’s Choice

2. Abby and Bing Woo have a small bakery shop that specializes in cookies.
They make only two kinds of
cookies – plain cookies and
cookies with icing. They need
to decide how many dozens of
each kind of cookies to make
for tomorrow.
One dozen of their plain cookies requires a pound of cookie dough (and no icing), while one dozen of their iced cookies requires 0.7 pounds of cookie dough and 0.4 pounds of icing.

3. The Woos know from experience that each dozen of the plain cookies requires about 0.1 hours of preparation time, and each dozen of the iced cookies requires about 0.15 hours of preparation time.
They also know that, no matter how many of each kind they make, they will be able to sell them all.

4. Their decision is limited by the following things:
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 tomorrow.
The amount of preparation time available – together they have 15 hours for cookie preparation.

5. Why on earth should the Woos care how many cookies of each kind they make?
$$$$$$$$
Well, you guessed it!
They want to make as much money as possible. They sell the plain cookies for $6.00 a dozen and it costs them $4.50 a dozen to make those cookies. The iced cookies sell for $7.00 a dozen and cost $5.00 a dozen to make.

6. What’s the profit on each dozen plain cookies they sell?
What’s the profit on each dozen iced cookies they sell?
They sell the plain cookies for $6.00 a dozen and it costs them $4.50 a dozen to make those cookies.
The iced cookies sell for $7.00 a dozen and cost $5.00 a dozen to make.

7. The Big Question Is…
How many dozens of each kind of cookie should Abby and Bing make so that their profit is as high as possible?
? ? ?

8. To begin answering The Big Question, find one combination of plain cookies and iced cookies that will satisfy all of the conditions in the problem.
Ingredients: They have 110 lbs of cookie dough.
They have 32 lbs of icing.
Time: They have 15 hours to work.
Oven Space: They can make 140 dozen cookies each day.
Each dozen of plain cookies takes 1 lb of cookie dough, no lbs of icing, 0.1 hours of prep time.
Each dozen of iced cookies takes 0.7lb of cookie dough, 0.4 lb of icing and 0.15 hours of prep time.
Find out how much profit the Woos will make on that combination of cookies.

9. Now find three more different combinations of cookies that fits the problem, but that makes a greater profit for the Woos.
Ingredients: They have 110 lbs of cookie dough.
They have 32 lbs of icing.
Time: They have 15 hours to work.
Oven Space: They can make 140 dozen cookies each day.
Each dozen of plain cookies takes 1 lb of cookie dough, no lbs of icing, 0.1 hours of prep time.
Each dozen of iced cookies takes 0.7lb of cookie dough, 0.4 lb of icing and 0.15 hours of prep time.

10. Day 1 A Simpler Cookie
The Woos have a rather complicated problem to solve.
Let’s make it simpler. Finding a solution to a simpler problem may lead to a method for solving the original problem.
Assume that the Woos still make plain cookies and cookies with icing.
Also assume that they still have
110 pounds of cookie dough
altogether to make both kinds
of cookies.

11. But now assume that they have an unlimited amount of both preparation time and icing and that they have an unlimited amount of space in their oven.
The other information is unchanged, and is as follows:
Each dozen plain cookies requires 1 lb cookie dough
Each dozen iced cookies requires 0.7 lbs cookie dough
The profit on the plain cookies is $1.50 a dozen.
The profit on the iced cookies is $2.00 a dozen.

12. As before, the Woos know that no matter how many of each kind they make, they will be able to sell them all.
1. Find at least five combinations of plain
and iced cookies that the Woos could
make without using more than 110 lbs
of cookie dough.
For each combination, find the profit that they would make.
2. From those 5 combinations, find the one
that you think would give the Woos the greatest
profit. Are there other combinations that would give a higher profit?