Each week Chemco can purchase unlimited quantities of raw material at $6/lb. 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 oz of input 1, requiring 2 hours of processing time and incurring $2 in processing costs. Each pound of raw material can yield 3 oz of input 2, requiring 2 hours of processing time and incurring $4 in processing costs.
Two production processes arc available. It takes 2 hours to run process 1, requiring 2 oz of input 1 and 1 oz of input 2. It costs $1 to run process 1. Each time process 1 is run 1 oz of product A and 1 oz of liquid waste arc produced. Each time process 2 is run requires 3 hours of processing time, 2 oz of input 2 and 1 oz of input 1. Process 2 yields 1 oz of product B and .8 oz 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 1,000 oz/week. One ounce of product C costs $4 to produce and sells for $11. One hour of processing time, 2 oz of input 1, and .8 oz of liquid waste arc needed to produce an ounce of product C. One unit of product D costs $5 to produce and sells for $7. One hour of processing lime, 2 oz of input 2, and 1.2 oz of liquid waste arc needed to produce an ounce of product D.
At most 5,000 oz of product A and 5,000 oz of product B can be sold each week, but weekly demand for products C and D is unlimited. Product A sells for $18/oz and product B sells for $24/oz. Each week 6,000 hours of processing time is available. Formulate an LP whose solution will tell Chemco how to maximize weekly profit.
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