Cardinal Manufacturing is seeking to optimize its profitability related to production of two main goods, hammers and shovels. In order to produce a lot of 100 hammers Cardinal needs 45 pounds of steel and 35 pounds of wood. The profit per lot of hammers is $150. In order to produce a lot of 100 shovels, Cardinal needs 75 pounds of steel and 85 pounds of wood. The profit per lot shovels is $240. The factory material throughput is limited to 800 pounds of steel and 1200 pounds of wood per day. One additional constraint is that the factory must produce at least 2 lots of each product per day. What is the optimal number of lots of each product and the resulting profit? Show your work in developing the optimized answer.

**Subject Mathematics Operations Research**