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Our paint store (OPS) sells 5 different paints to consumers: Red, Yellow, Green, Brown, and Blue

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Our paint store (OPS) sells 5 different paints to consumers: Red, Yellow, Green, Brown, and Blue. Demand of each color paint is normally distributed with monthly mean (gallons) and standard deviation summarized in Table 1. Annual holding cost rate is 25%. Each order incurs an ordering setup (fix) cost of $1,000, and lead time is 2 months. Our paint store (OPS) wants the probability of stocking out (1-SL) to be no more than 5% (use z=1.65). Table 1: Dem and (Gallon/Month) Color Mean Demand Standard Deviation of Demand Red 20 10 Yellow 40 20 Green 32 15 Brown 44 25 Blue 50 30 (a) Assume that each color paint's inventory is managed independently each color paint determines its order quantity and safety stock individually). Cost per gallon of paint is $20 regardless of color. (a.1) Let @j=Red, Yellow, Green, Brown, Blue denote economic order quantity (EOQ) of the color paint j. For example, Red =EOQ of color paint Red. Also let 0* = gRed + Yellow + Brown + Green + Blue be the total EOQ of 5 color paints. + = Compute EOQ for each color. Rad = ?, = Yelbw = ?, Brown = ?, Green=?, Blue = ?. = = What should be the total EOQ for 5 colors combined? * = ? (a.2) Let denote safety stock stock (SS) of the color paint j. paint ). Also let Is = 1ked + 1ellow + Iown + Igren + Tutu be total the SS of 5 color paints. + Compute SS for each color. I green = ?, rellow = ?, 1 Town = ?, Blue = ?, rekel = ?. = we S S = = S > > What should be the total SS for 5 colors combined? Is = ? (a.3) Let I I = Red + Yellow denote average inventory (1) of the color paint ). Also let + Green + y Blus be the total 1 of 5 color paints. = + Brown + Compute / for each color. [Green = ?, Kellow = ?, Bown = ?, Blue = ?, Red = ?. = = = What should be the total / for 5 colors combined? 1 = ? (a.4) Let AIC denote annual inventory cost (AIC) of the color paint j. Also let AIC = AICPod + AICYlbw + AICROWN + AIC Green + AICA be the total AIC of 5 color paints. Red Yellow Awe Compute AIC for each color. AICM = ?, Aiclellow = ?, AICROwn = ?, AICPUe = ?, Aiched = ?. = = = = What should be the total A/C for 5 colors combined? AIC = ?