[20 points] A factory has two production lines available to make a product. The first line can produce one unit of the product in t1 hours at a cost of c1. The second requires t2 hours at a cost of c2. The plant manager wishes to find the least costly way to produce b units in a total of at most T hours. Determine the integer number of units of product, x1, to produce on line 1, and the integer number of units of product, x2, to produce on line 2. Identify each of the following for this design problem: ? a. The input parameters ? b. The decision variables ? c. The objective function ? d. The constraints