A hospital patient is required to have at least 90 units of drug I and 120 units of drug II. The drugs are both contained in two substances \(S_{1}\) and \(S_{2}\). Suppose that a gram of \(S_{1}\) contains 6 units of drug I and 4 units of drug II, and a gram of \(S_{2}\) contains 3 units of drug I and 3 units of drug II. But in addition, each gram of \(S_{1}\) contains 2 units of a mildly toxic drug and each gram of \(S_{2}\) contains 1 unit of this other undesirable drug. How much of each substance should be given to the patient to achieve the medication requirements with minimal dosage of the toxin? How much of the toxin does the patient receive with this optimal mixture?