### What is the maximum annual profit that can be obtained

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A catalytic process uses a catalyst which must be regenerated periodically because of reduction in conversion efficiency. The cost for one regeneration is constant at \$800. This figure includes all shutdown and startup costs, as well as the cost for the actual regeneration. The feed rate to the reactor is maintained constant at 150 lb/day, and the cost for the feed material is \$2.50 per pound. The daily costs for operation are \$300, and tixed charges plus general overhead costs are \$100,090 per year. Tests on the catalyst show that the yield of product as pounds of product per pound of feed during the first day of tgeration with the regenerated catalyst is 0.87, and the yield decreases as 0.87/(θD)0.25, where θD, 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 \$14.08 per pound, and the plant operates 300 days per year. Assuming no costs are involved other than those mentioned, what is the maximum annual profit that can be obtained under these conditions?

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