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Charleys Ice Cream (CIC) specializes in small-batch homemade ice cream. The first stage in ice cream making is the blending of ingredients to obtain a 50 pounds mix, which meets pre-specified requirements based on 7 constituents. The ingredients currently used in CICs ice cream are shown in Table 1, while Table 2 shows the constituent requirements, which are based on the percentages of a 50-pound batch.

Table 1: Ingredients in Pounds Ingredient Pounds Plastic cream 9.73 Sugared frozen egg yolk 0.44 Water 25.24 Skim milk powder 3.03 Stabilizer 0.12 Liquid sugar 11.27 Emulsifier 0.07

Table 2: Requirements by Constituent Constituent Requirement Fat 16.00% Serum Solids 8.00% Sugar Solids 16.00% Egg Solids 0.35% Stabilizer 0.25% Emulsifier 0.15% Water 59.25%

There are additional ingredients that could be used to make a batch of ice cream. In other words, there are other combinations of ingredients that could meet the 50-pound batch size and the constituent requirements. These additional ingredients are shown in Table 3 along with the current price per pound.

Table 3: Ingredient costs in $ per pound

40% Cream($1.19) 23% Cream($0.70) Butter($2.32) Plastic Cream($2.30) Butter Oil($2.87) 4% Milk($0.25) Cond Skim Milk($0.35) Skim Milk Powder($0.65) Liquid Sugar($0.25) Sugared Frozen Egg Yolk($1.75) Powdered Egg Yolk($4.45) Stabilizer($2.45) Emulsifier($1.65) Water($0.01) Each ingredient contributes to the constant requirement differently. For example, there are many sources of fat. The input/output matrix showing the pounds of each of the 7 constituents provided by each of the 14 potential ingredients in shown in Table 4. For example, one pound of 40% cream adds 0.4 pound of fat, 0.1 pound of serum solids and 0.5 pounds of water to the mix. In addition, one pound of skim milk powder adds one pound of serum solids. For several years, CIC has been using the recipe shown in Table 1 for 50 pounds batches.

Table 4: Input/output ratios for 14 ingredients by 7 constituents

40% Cream (Fat 0.4, Serum Solids 0.1, Water 0.5)

23% Cream (Fat 0.2, Water 0.8)

Butter (Fat 0.8, Water 0.2)

Plastic Cream (Fat 0.8, Serum Solids 0.1, Water 0.1)

Butter Oil (Fat 0.9, Water 0.1)

4% Milk (Fat 0.1, Serum Solids 0.1, Water 0.8)

Cond Skim Milk (Serum Solids 0.3, Water 0.7)

Skim Milk Powder (Serum Solids 1.0)

Liquid Sugar (Sugar Solids 0.7, Water 0.3)

Sugared Frozen Egg Yolk (Fat 0.5, Sugar Solids 0.1, Egg Solids 0.4)

Powdered Egg Yolk (Fat 0.5, Egg Solids 0.5)

Stabilizer (Stabilizer 1.0)

Emulsifier (Emulsifier 1.0)

Water (Water 1.0)

1. Based on the information above, determine the cost of the original recipe.

a. HINT: Later, you will be asked to use linear programming to determine additional recipes. Before you are asked to utilize Solver, develop a worksheet that clearly shows the 14 possible decisions cells along with the ingredients listed in Table 1. In addition, formulate your worksheet where you are checking that the 50 pound batch requirement is met, along with the percent recruitments of constituent shown in Table 2 are met. In other words, set up the spreadsheet as if you were setting it up for a linear program. However, for this part of the problem, you will not need to run Solver. That portion of the problem will come later. b. HINT: Since the batch size (50 pounds) is a specified constant, you may use it in the divisor of formulas for actual percentages of constituents without creating a nonlinear ratio. In other words, to ensure that the current recipe shown in Table 1 meets the percentage constraints shown in Table 2, you should divide the constituent by 50 pounds. Remember, you cannot have decision cells in the numerator of a calculation, but there is no rule about a constant in the numerator of a calculated cell.

2. CIC proposes to use linear programming to determine if there is a better mixture of ingredients that is more cost effective that will still met the constituent requirements shown in Table 2. Create a copy of your original worksheet to develop a linear program and determine the minimum cost using all 14 possible ingredients to meet all requirements.

3. CIC is also considering loosening the requirements for the 7 constituents from exact percentages to the ranges shown in Table 5. Create a copy of your solution for part 2. Use Solver to determine the minimum cost recipe based on the proposed ranges of percentages for the constituents.

4. Create a worksheet to summarize the ingredients and the costs of the three recipes above. In other words, you will have 4 worksheets for the solution to this problem. 1) Original Recipe with Total Cost (no Solver), 2) Exact Percentages Recipe with Total Cost (Solver Req.), 3) Proposed Ranges Recipe with Total Cost (Solver Req.), and 4) a Summary that shows the 3 recipes with their total cost.