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Richelieu Specialty Paints has begun making paints for the interior design market. The company starts the process by blending four base paint mixes that they buy from major manufacturers. They then add other components to finish off the paint mix to customer specifications. Each of the four base mixes includes pigment, solvent and three additives. When Richelieu blends the four base mixes they want the final product to be within these specifications (these numbers are a percentage of total volume): • Pigment: 25% ≤ x ≤ 30% • Solvent: 60% ≤ x ≤ 65% • Additive 1: 3% ≤ x ≤ 5% • Additive 2: 5% ≤ x ≤ 7% • Additive 3: 1% ≤ x ≤ 3% 4 The specifications of each of the four base mixes before they are blended together is: Base 1 Base 2 Base 3 Base 4 Pigment Volume 30.0% 25.0% 25.0% 30.0% Solvent Volume 48.0% 60.0% 67.5% 55.0% Additive 1 Volume 10.0% 5.0% 0.0% 5.0% Additive 2 Volume 6.0% 5.0% 2.0% 10.0% Additive 3 Volume 6.0% 5.0% 5.5% 0.0% Unit Cost $15 $25 $20 $40 Recommend what percentage of each base mix should be included in the blend to achieve specifications listed, keeping input costs as low as possible. Base mix 3 is purchased overseas and thus the price fluctuates due to currency exchange rates. Comment on how the percentage of each base included in the blend would change if the cost for mix 3 rises to $30 per unit and note what would happen to total cost in this situation.
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