Case Study: Schneiders Sweet Shop

Schneiders Sweet Shop specializes in homemade candies and ice cream. Schneider produces its ice cream in-house, in batches of 50 ponds. The first stage in ice cream making is the blending of ingredients to obtain a mix which meets pre-specified requirements on the percentage of certain constituents of the mix. The desired composition is as follows:

Fat	16.00%
Serum solids	8.00%
Sugar solids	16.00%
Egg solids	0.35%
Stabilizer	0.25%
Emulsifier	0.15%
Water	59.25%

The mix can be composed of ingredients from the following list:

Ingredients Costs ($/lb)
40% Cream	$1.19
25% Cream	0.70
Butter	2.32
Plastic cream	2.30
Butter oil	2.87
4% milk	0.25
Skim condensed milk	0.35
Skim milk power	0.65
Liquid sugar	0.25
Sugared frozen fresh egg yolk	1.75
Powdered egg yolk	4.45
Stabilizer	2.45
Emulsifier	1.68
Water	0.00

The number of pounds of a constituents found in a pound of an ingredient is shown in the next list. Note that a pound of stabilizer contributes only to the stabilizer requirements (on pound), one pound of emulsifier contributes only to the emulsifier requirements (one pound), and that water contributes only to the water requirements (one pound).

Constituent	Ingredient
	1	2	3	4	5	6	7	8	9	10	11	12	13	14
1	0.4	0.2	0.8	0.8	0.9	0.1				0.5	0.6
2	0.1			0.1		0.1	0.3	1.0
3									0.7	0.1
4										0.4	0.4
5												1.0
6													1.0
7	0.5	0.8	0.2	0.1	0.1	0.8	0.7		0.3					1.0

Young Jack Schneider has recently acquired the shop from his father. Jacks father has in the past used the following mixture: 9.73 pounds of plastic cream, 3.03 pounds of skim milk powder, 11.37 pounds of liquid sugar, 0.44 pounds of sugared frozen free egg yolk, 0.12 pounds of stabilizer, 0.07 pounds of emulsifier, and 25.24 pounds of water. (The scale at Schneiders is only accurate to 100^th of a pound.) Jack feels that perhaps it is possible to produce the ice cream in a more cost-effective manner. He would like to find the cheapest mix for producing a batch of ice cream, which meets the requirements specified above.

Jack is also curious about the cost effect of being a little flexible in the requirements listed above. He wants to know the cheapest mix if the composition meets the following tolerance:

Fat	15.00 - 17.00%
Serum solids	7.00 - 9.00%
Sugar solids	15.50 - 16.50%
Egg solids	0.30 - 0.40%
Stabilizer	0.20 - 0.30%
Emulsifier	0.10 - 0.20%
Water	58.00 - 59.50%

Managerial Report

Write a managerial report which compares the cost of Papa Jacks approach to (a) the cost-minimized approach using the desired composition and (b) the cost-minimized approach with the more flexible requirements. Include the following in your report:

The cost of 50 pounds of ice cream under each of the three approaches.

The amount of each ingredient used in the mix for each of the three approaches.

A recommendation as to which approach should be used.