Each week, Chemco can purchase unlimited quantities of raw material at $6 per pound. Each pound of purchased raw material can be used to produce either input 1 or input 2. Each pound of raw material can yield 2 ounces of input 1, requiring 2 hours of processing time and incurring $2 in processing costs. Each pound of raw material can yield 3 ounces of input 2, requiring 2 hours of processing time and incurring $4 in processing costs. Two production processes are available. It takes 2 hours to run process 1, requiring 2 ounces of input 1 and 1 ounce of input 2. It costs $1 to run process 1. Each time process 1 is run, 1 ounce of product A and 1 ounce of liquid waste are produced. Each time process 2 is run requires 3 hours of processing time, 2 ounces of input 2, and 1 ounce of input 1. Each process 2 run yields 1 ounce of product B and 0.8 ounce of liquid waste. Process 2 incurs $8 in costs. Chemco can dispose of liquid waste in the Port Charles River or use the waste to produce product C or product D. Government regulations limit the amount of waste Chemco is allowed to dump into the river to 5000 ounces per week.
Each ounce of product C costs $4 to produce and sells for $18. Producing 1 ounce of product C requires 1 hour of processing time, 2 ounces of input 1, and 0.8 ounce of liquid waste. Each ounce of product D costs $5 to produce and sells for $12. Producing 1 ounce of product D requires 1 hour of processing time, 2 ounces of input 2, and 1.2 ounces of liquid waste. At most, 7000 ounces of product A and 5000 ounces of product B can be sold each week, but weekly demand for products C and D is unlimited. Product A sells for $22 per ounce and product B sells for $24 per ounce. Each week, 25,000 hours of processing time are available. Determine how Chemco can maximize its weekly profit.
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