Ice Cream Delights

Ice cream delights creates their own unique blend of homemade ice cream. Ice Cream Delights creates its ice cream in batches of 60 pounds. They first blend the ingredients to create a mix which meets the requirements of the percentages of constituents for the mix. Ice cream delights wants to make the mixture as follows:

1.	Fat	15.00%
2.	Milk solids-not-fat	8.00%
3.	Glucose	18.00%
4.	Whole egg solids	.5%
5.	Thickener	.35%
6.	Emulsifying Agents	.15%
7.	Water	58%

The following ingredients can be used to make the ice cream:

Ingredient Cost ($/lb.)
1. 50% Cream	$.78
2. 25% Cream	.70
3. Margarine	2.32
4. Artificial cream	2.30
5. Soybean Oil	2.07
6. Whole Milk	.25
7. Condensed milk	.35
8. Powdered Milk	.65
9. Sugar	.35
10. Fresh eggs	1.75
11. Powdered eggs	4.45
12. Thickener	2.45
13. Emulsifying Agent	1.68
14. Water	.00

The number of pounds of a constituent found in a pound of an ingredient is shown in the next list. One pound of thickener contributes only to the thickening requirement (one pound), one pound of emulsifying agent contributes only to the emulsifying agent requirement (one pound), and that water contributes only to the water requirement (one pound).

Constituent	Ingredient
PRIVATE	1	2	3	4	5	6	7	8	9	10	11	12	13	14
1	.35	.3	.7	.75	.95	.1				.4	.7
2	.15			.1		.2	.35	1
3									.8	.1
4										.5	.3
5												1
6													1
7	.5	.7	.3	.15	.05	.7	.65		.2					1

1. A new manager has taken ownership of the business. The last owner previously used the following ingredients: 11.68 pounds of artificial cream, 3.64 pounds of powdered milk, 13.64 pounds of sugar, 0.53 pounds of fresh eggs, 0.14 pounds of thickener, 0.08 pounds of emulsifying agent, and 30.22 pounds of water. The new manager believes that using an LP model, it is possible to produce the ice cream more cost-effectively. She would like to find the cheapest mix for producing the ice cream while still meeting the requirements shown above.

2. The new manager is also curious how much more money could be save by being a little more flexible in the requirements listed above. She wants to find the cheapest mix with the following tolerances.

1.	Fat		14.0016.00%
2.	Milk solids-not-fat		7.009.00%
3.	Glucose		17.0019.00%
4.	Whole egg solids		.40.60%
5.	Thickener		.25.45%
6.	Emulsifying Agents		.05.25%
7.	Water		57.0059.00%