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.

Case Problem 2 SCHNEIDER'S SWEET SHOP Schneider's Sweet Shop specializes in homemade candies and ice cream. Schneider produces its 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 require- ments on the percentages of certain constituents of the mix. The desired composition is as follows: 1. Fat 2. Serum solids 3. Sugar solids 4. Egg solids 5. Stabilizer 6. Emulsifier 7. Water 16.00% 8.0096 16.00% .35% .25% 15% 59.25% The mix can be composed of ingredients from the following list: Ingredient Cost (S/1b.) 1. 40% Cream 2. 23% Cream 3. Butter 4. Plastic cream 5. Butter oil 6. 4% Milk 7. Skim condensed milk 8. Skim milk powder 9. Liquid sugar 10. Sugared frozen fresh egg yolk 11. Powdered egg yolk 12. Stabilizer 13. Emulsifier 14. Water $1.19 .70 2.32 2.30 2.87 25 .35 .65 .25 1.75 4.45 2.45 1.68 .00 The number of pounds of a constituent found in a pound of an ingredient is shown in the next list. Note that a pound of stabilizer contributes only to the stabilizer requirement (one pound), one pound of emulsifier contributes only to the emulsifier requirement (one pound). and that water contributes only to the water requirement (one pound). Constituent PRIVATE 1 .4 .1 2 .2 3 .8 4 .8 .1 Ingredient 5 6 7 8 9 10 11 12 13 14 .9 .1 .5 .6 .1 3 1 .7 .1 .4 .4 3 7 5 .8 2.1 1.8 7 .3 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, 0.44 pounds of sugared frozen fresh egg yolk, 0.12 pounds of stabilizer, 0.07 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 cheap- est 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 require- ments listed above. He wants to know the cheapest mix if the composition meets the follow- ing tolerances: 1. Fat 2. Serum solids 3. Sugar solids 4. Egg solids 5. Stabilizer 6. Emulsifier 7. Water 15.00-17.00% 7.00-9.00% 15.50-16.50% .30-40% .20-30% .10-20% 58.00-59.50% Managerial Report Write a managerial report which compares the cost of Papa Jack's 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: 1. The cost of 50 pounds of 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