A manufacturer of lapel buttons test marketed a new item at a university. It was found that 1,000 items could be sold if they were priced at $4, but only 600 items could be sold if the price were raised to $8. On the other hand, the manufacturer finds that 400 items can be supplied at $1 each. If they were supplied at $9 each, overtime shifts could be used to raise the supply to 800 items. What is the optimum price for the items?