An organic chemical is produced by a batch process. In this process, chemicals X and Y react to form chemical Z. Since the reaction rate is very high, the total time required per batch has been found to be independent of the amounts of the materials, and each batch requires 2 h, including time for charging, heating, and dumping. The following equation shows the relation between the pounds of Z produced (lb,) and the pounds of X (lb,) and Y (lb,) supplied:
Chemical X costs $0.09 per pound. Chemical Y costs $0.04 per pound. Chemical Z sells for $0.80 per pound. If one-half of the selling price for chemical Z is due to costs other than for raw materials, what is the maximum profit obtainable per pound of chemical Z?