Quart Industries produces a variety of bottled food products at its various plants. At its Americus plant, it produces two products, peanut butter and apple butter. There are two scarce resources at this plant: packaging capacity and sterilization capacity. Both have a capacity of 40 hours per week. Production of 1000 jars of peanut butter requires 4 hours of sterilizer time and 5 hours of packaging time, whereas it takes 6 hours of sterilizer time and 4 hours of packaging time to produce 1000 jars of apple butter. The profit contributions per 1000 jars for the two products are $1100 and $1300, respectively. Apple butter preparation requires a boil-down process best done in batches of at least 5000 jars. Thus, apple butter production during the week should be either 0, or 5000 or more jars. How much should be produced this week of each product? [Your solution needs to explain how you deal with the apple butter constraint, and how you would come up with the final solution]