Question: A catalytic process uses a catalyst which must be regenerated periodically because of reduc- tion in conversion efficiency. The cost for one regeneration is constant
A catalytic process uses a catalyst which must be regenerated periodically because of reduc- tion in conversion efficiency. The cost for one regeneration is constant at $800. This figure in- cludes all shutdown and start-up costs as well as the cost for the actual regeneration. The feed rate to the reactor is maintained constant at 70 kg/day, and the cost for the feed material is $5.50 per kilogram. The daily costs for operation are $300, and fixed charges plus general overhead costs are $100,000 per year. Tests on the catalyst show that the yield of product as kilograms of product per kilogram of feed during the first day of operation with the regener- ated catalyst is 0.87, and the yield decreases as O.87/0y25, where 6D is the time in operation expressed in days. The time necessary to shut down the unit, replace the catalyst, and start-up the unit is negligible. The value of the product is $31.00 per kilogram, and the plant operates 300 days/yr. Assuming no costs are involved other than those mentioned, what is the maxi- mum annual profit that can be obtained under these conditions?
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