4) The Wod Chemical Company produces a chemical compound that is used as a lawn fertilizer. The compound can be produced at a rate of 10,000 pounds per day. Annual

demand for the compound is 0.8 million pounds per year. The fixed cost of setting up for a production run of the chemical is $1,500, and the variable cost of production is$3 per pound. The company uses an interest rate of 25 percent to account for the cost of capital, and the costs of storage and handling of the chemical amount to 12 percent of the value. Assume that there are 250 working days in a year. a) What is the optimal size of the production run for this particular compound? b) What proportion of each production cycle consists of up-time and what proportion consists of downtime? c) What is the average annual cost of holding and setup attributed to this item? If the compound sells for $3.50 per pound, what is the annual profit the company is realizing from this item? d) Determine the batch size that would result if you assumed that the production rate was infinite. What is the additional average annual cost that would be incurred using this batch size rather than the one you found in part a?

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