Dear IMC: As you know. Chemproe, Inc. is a premier manufacturer and reprocessor of chemicals and chemical waste. Further, as has been recently highlighted on the local news, we are in the process of expanding our Lonline, Skanebra chemical manufacturing plant to add two or three new products to our elegantly packaged and painstakingly marketed product line-which will result in our hiring at least four local workers. Our engineers have, however, determined that for these products to be successful in today's competitive market we must be careful to obtain the absolute highest profit possible. We are, for reasons of corporate secrecy, unable to reveal the exact names of the products that we will be producing, and therefore refer to them herein as products X and Y (for the case in which two products are produced), respectively. We will be manufacturing x and y units of these per day, and expect to realize a profit of a and b dollars per unit on each of the products (again, we are unable to divulge the actual values determined by our marketing department). The actual number of units of these that we can produce is, however, limited by the number of person- hours that the workers have available. This will be L person-hours. To manufacture one unit of X requiresc person-hours, and the hours required for more units is proportional to the number of units of X produced. For the second product, however, economies of scale are much more pronounced, so that the number of person-hours re-quired to produce y units of it is proportional to y P (where 0