Using this Case Problem, develop the linear programming model. Then, discuss the pros and cons of using this mathematical model in making a managerial decision for this kind of problems.

From Chapter 4 Case Study 2- An Introduction to Management Science- A Qualitative Approach to Decision Making 14e

Schneider's sweet shop specializes in homade candies and ice cream. Schneider produces its ice cream in-house, in batches of 50 pounds. The first stage in ice cream making is blending of the 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. Stabalizer .25%

6. Emulsifier .15%

7. Water 59.25 %

The mix can be composed from the following list

Ingredient Cost ($/lb)

1. 40% Cream 1.19

2. 23% Cream .70

3. Butter 2.32

4.Plastic Cream 2.30

5. Butter Oil 2.87

6. 4% milk .25

7. Skim condensed milk .35

8. Skim milk powder .65

9. Liquid Sugar .25

10. Sugared frozen fresh egg yolk 1.75

11. Powdered egg yolk 4.45

12. Stabalizer 2.45

13. Emulsifier 1.68

14. Water .00

The number of pounds of a constituent found in a pound of an ingredient is show before. Note that a pound of stabalizer contributes only to the stabalizer 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 .4 .2 .8 .8 .9 .1 .5 .6

2 .1 .1 .3 .1

3 .7 .1

4 .4 .4

5 1

6 1

7 .5 .8 .2 .1 .1 .8 .7 .3 1

Young Jack Schneider has recently acquired the shop from his father. Jack's 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,. 44 pounds of sugared frozen fresh egg yolk, .12 pounds of stabalizer, .07 pounds of emulsifier, and 25.24 pounds of water. (The scale at Schneider's is only accurate to 100th 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 more flexible in the requirements listed above. He wants to konw the cheapest mix if the composition meets the following tolerances:

1) Fat 15-17%

2) Serum Solids 7-9%

3) Sugar Solids 15.5-16.5%

4) Egg Solids .3-.4%

5) Stabalizer .2-.3%

6) Emulsifier .1-.2%

7) Water 58-59.5%