This problem involves three chemicals a, b, c. you have a liters of chemical a, b liters of chemical b, and c liters of chemical c (for each chemical you have a pure solution). there are n potential customers. the i-th customer wants di liters of an ai : bi : ci mixture of chemicals a, b, c and is willing to pay pi dollars per liter of the desired mixture. you need cash. you want to get as much money as possible by creating mixtures and selling them to the potential customers. the customers will purchase your mixture even if you only partially satisfy their demand (for example, if a customer wants 3 liters of a 7 : 8 : 9 mixture and is willing to pay $8 per liter and you supply 1.2 liters of a 7 : 8 : 9 mixture they will pay you $9.6). give a linear program for the problem. clearly describe the variables in your linear program.