Answer the following question, it's a linear programming question.

1. 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 requirements on the percentages of certain constituents of the mix. The desired composition is as follows: Table 1: Constituent Fat 16% Serum solids 8% Sugar solids 16% Egg solids 0.35% Stabilizer 0.25% Emulsifier 0.15% Water 59.25% The mix can be composed of ingredients from the following list: Table 2: Ingredients Ingredient Cost ($/lb.) 40% Cream $1.19 23% 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 powder $0.65 Liquid sugar $0.25 Sugared frozen fresh egg yolk $1.75 11 Powdered egg yolk $4.45 12 Stabilizer $2.45 13 Emulsifier $1.68 14 Water $0.00 The number of pounds of a constituent found in a pound of an ingredient is shown in the next list. 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. Jack feels that 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 meet the requirements specified above.Constituent 1 2 4 6 7 8 9 10 11 12 13 14 4 2 8 8 5 6 .1 .1 3 1 .7 .4 .4 1 .5 .8 2 1 1 .8 .7 .3 Jack is also curious about the cost effect of being a little more flexible in the requirements listed above. He wants to know the cheapest mix if the composition meets the following tolerances: Table 3: Constituent Fat 15% - 17% Serum solids 7% - 9% Sugar solids 15.5% - 16.5% Egg solids 0.3% - 0.4% Stabilizer 0.2% - 0.3% Emulsifier 0.1% - 0.2% Water 58% - 59.5% (a) Formulate the problem as a LP model.(b) Write a managerial report which compares i. the cost of Papa Jack's approach; ii. the cost-minimized approach using the desired compositions; and iii. the cost-minimized approach with the more flexible requirements. Note: 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.2. Hart Fenture Capital {HMS} specializes in providing venture capital for software development and Internet applications. lSurrently H'v'G has two investment opportunities: on Security Systems, a rm that needs additional capital to develop an Internet security software package, and In Market Analysis, a market research company that needs additional capital to develop a software package for conducting customer satisfaction surveys. In exchange for Security Systems stock, the rm has asked EVE to provide $ in year 1, $El} in year 2, and SEE-l in year 3 over the coming three-year period. In exchange for their stock, Market Analysis has asked HUG to provide Sll in year 1, SSE-Silt]?! in year 2, and savanna in year 3 over the same three-year period. HVG believes that both investment opportunities are worth pursuing. However, because of other investments, they are willing to commit at most $300,003 for both projects in the rst year, at most $'F[l,l][l[l in the second year, and S51},lll} in the third year. HVG's nancial analysis team reviewed both projects and recommended that the company's objective should be to maximise the net present value of the total investment in Security Systems and Market Analysis. The net present value takes into account the estimated value of the stock at the end of the three-year period as well as the capital outows that are necessary during each of the three years. Using an 3% rate of return, H'J's nancial analysis team estimates that 1% funding of the Security Systems project has a net present value of $1,8,m, and I' funding of the Market Analysis project has a net present value of $1,,l EVE has the option to fund any percentage of the Security Systems and Market Analysis projects. For example, if HVG decides to fund di of the Security Systems project, invest- ments of [L40 3: $603, U111} = $2413, Dill} would be required in year 1, Ill-ill x m, i} = $29k}, Dill] would be required in year 2, and [1.413 3-: $2513, [Ill = $1, would be required in year 3. In this case, the net present value of the Security Systems project would be [hit] 1-: $1,S,[l[l = $2443, Hill]. The investment amounts and the net present value for partial funding of the Market Analysis project would be computed in the same manner. {a} Formulate the HVU's investment problem a LP model. (b) Prepare a report that presents your findings and recommendations. Include a consider- ation of the following items: i. What is the recommended percentage of each project that HVC should fund and the net present value of the total investment? ii. What capital allocation plan for Security Systems and Market Analysis for the coming three-year period and the total HVC investment each year would you rec- ommend? iii. What effect, if any, would HVC's willingness to commit an additional $100,000 during the first year have on the recommended percentage of each project that HVC should fund? iv. What would the capital allocation plan look like if an additional $100,000 is made available? v. What is your recommendation as to whether HVC should commit the additional $100,000 in the first year