Johnson Candy Company
Having discussed a nationwide product and its consequences, you decide to go a local institution to reward yourself with a delicious ice cream bar. You start talking to the most recent owner, Sally, and upon finding out that you are studying how to make better business decisions, she opens up about some recent ideas she has had about improving the business.
Background
Johnson Candy Company makes homemade candy and ice cream. They produce their ice cream in-house, in batches of 50 pounds. The first stage in ice cream making is the blending of ingredients to obtain a mix, which meets pre-specified requirements on the percentages of certain constituents of the mix. The desired composition is as follows:
|
1. Fat
|
16%
|
|
2. Serum Solids
|
8%
|
|
3. Sugar Solids
|
16%
|
|
4. Egg Solids
|
.35%
|
|
5. Stabilizer
|
.25%
|
|
6. Emulsifier
|
.15%
|
|
7. Water
|
59.25%
|
The mix can be composed of ingredients from the following list:
|
Ingredient Cost ($/lb)
|
|
|
40% Cream
|
$1.19
|
|
23% Cream
|
.70
|
|
Butter
|
2.32
|
|
Plastic Cream
|
2.30
|
|
Butter Oil
|
2.87
|
|
4% Milk
|
.25
|
|
Skim Condensed Milk
|
.35
|
|
Skim Milk Powder
|
.65
|
|
Liquid Sugar
|
.25
|
|
Sugared Frozen Fresh Egg Yolk
|
1.75
|
|
Powdered Egg Yolk
|
4.45
|
|
Stabilizer
|
2.45
|
|
Emulsifier
|
1.68
|
|
Water
|
.00
|
The number of pounds of a constituent found in a pound of an ingredient is shown below. Note that a pound of stabilizer contributes only to the stabilizer requirement (1 pound). 1 pound of emulsifier contributes only to the emulsifier requirement 1 pound, and that water contributed only to the water requirement (1 pound).
|
Constituent
|
Ingredient
|
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
13
|
14
|
|
1
|
.4
|
.2
|
.8
|
.8
|
.9
|
.1
|
|
|
|
.5
|
.6
|
|
|
|
|
2
|
.1
|
|
|
.1
|
|
.1
|
.3
|
1
|
|
|
|
|
|
|
|
3
|
|
|
|
|
|
|
|
|
.7
|
.1
|
|
|
|
|
|
4
|
|
|
|
|
|
|
|
|
|
.4
|
.4
|
|
|
|
|
5
|
|
|
|
|
|
|
|
|
|
|
|
1
|
|
|
|
6
|
|
|
|
|
|
|
|
|
|
|
|
|
1
|
|
|
7
|
.5
|
.8
|
.2
|
.1
|
.1
|
.8
|
.7
|
|
.3
|
|
|
|
|
1
|
The original formula for the ice cream is: 9.73 pounds of Plastic Cream, 3.03 pounds of Skim Milk Powder, 11.37 pounds of Liquid Sugar, .44 pounds of Sugared Frozen Fresh Egg Yolk, .12 pounds of Stabilizer, .07 pounds of Emulsifier, and 25.24 pounds of water.
Sally is interested in producing the ice cream more cost-effectively, finding the cheapest mix for producing a batch of ice cream which meets the requirements specified above. She is also interested in finding out about the consequences of relaxing the ice cream composition to the following tolerances:
|
1. Fat
|
15-17%
|
|
2. Serum Solids
|
7-9%
|
|
3. Sugar Solids
|
15.5-16.5%
|
|
4. Egg Solids
|
.30-.40%
|
|
5. Stabilizer
|
.20-.30%
|
|
6. Emulsifier
|
.10-.20%
|
|
7. Water
|
58-59.50%
|
In exchange for a year's worth of ice cream bars, you agree to help Sally out. Provide a report that compares the old owner's approach to (a) cost-minimized approach using the desired composition and (b) a cost-minimized approach with the more flexible requirements. Include the following in your report:
1) The cost of 50 pounds if ice cream under each of the three approaches.
2) The amount of each ingredient used in the mix for each of the three approaches.
3) A recommendation as to which approach should be used.