3. Suppose you are an IE in chemical plant that makes a certain chemical in batches of size 1000 gallons. The main quali

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3 Suppose You Are An Ie In Chemical Plant That Makes A Certain Chemical In Batches Of Size 1000 Gallons The Main Quali 1 (81.43 KiB) Viewed 34 times

3. Suppose you are an IE in chemical plant that makes a certain chemical in batches of size 1000 gallons. The main quality characteristic of a batch is the purity, we will call this X. You just completed a quality control study that found X to be N(u=0.90, ² 0.0001). Purity is important because it determines the selling price of a gallon of the chemical. Selling prices are as follows: X < 0.89 0.89 < X < 0.91 X > 0.91 $0.60 / gallon $0.80/gallon $1.00/gallon Your plant produces 1000 batches of this product per month. Write an R function to determine your monthly revenue. Structure it like this: levels = c(0.89, 0.91) price = c(0.6, 0.8, 1.0) moments = c(μ, o) quantity = c(1000, 1000) #cutoff levels for pricing # $ per gallon for different pricing levels # mean and standard deviation of normal #number of batches per month, number of gallons per batch rev <-function(moments, levels, price){ # Find expected number of batches in each pricing level # Compute total revenue from selling batches in each pricing level # Compute total revenue and return } Use this function to answer the following questions: a. When the process mean is centered at 0.90, what is expected monthly revenue? b. Suppose the process mean shifts from 0.90 to 0.88. How much money would your company lose every month? c. Suppose without maintenance (which costs $40,000), the process mean shifts downward at a rate of 1/2 standard deviations per month. When maintenance occurs, the process mean is reset to 0.90. Assuming you can do at most one maintenance per month, how often should you do maintenance to optimize yearly revenue?