2. A small firm specializes in making five types of spare automo- bile parts. Each part is first cast from iron in the casting shop and then sent to finishing shop where holes are drilled, surfaces are turned, and edges are ground. The required worker-hours (per 100 units) for each of the parts of the two shops are shown in the table below: Part 1 Casting 2 Finishing 3 2 1 2 3 332 3 ce 4 3 1 5 1 1 Profits from the parts are $30, $20, $40, $25, and $10 (per 100 units), respectively. The capacities of casting and finish- ing shops over the next month are 700 and 1000 worker-hours, respectively. Formulate the LP problem of determining the quantities of each spare part to be made during the the month so as to maximize profit. Define each variable you choose to ue, but do not solve the LP problem.