A furniture manufacturer makes two kinds of furniture chairs and sofas. The production process has three operations: carpentry, finishing, and upholstery. The labor required for each operation varies. To manufacture a chair requires 6-hours of carpentry, 1-hour of finishing, and 2-hours of upholstery. To manufacture a sofa requires 3-hours of carpentry, 1-hour of finishing, and 6-hours of upholstery. Due to limited availability of skill, on each day, we have available 96-hours of carpentry labor, 18-hours of finishing labor and 72-hours of upholstery labor. We make $80 profit per chair, and $70 profit per sofa. How many chairs and sofas we should manufacture per day to maximize profit? Show work (don't just email two numbers). A soup manufacturer sells 16oz cans of soup. They would like to minimize the amount of metal used in the construction of the can. What are the dimensions of a 16oz can that uses the least amount of metal? Show work.