Problem 4. In order to treat a certain bacterial infection, a combination of two drugs is used. Studies have shown that the duration of the infection in laboratory tests can be modeled by T: 352423,;2 18x24y+2my+ 120 Where a: is the dose of the rst drug (in hundreds of milligrams) and y is the dose of the second drug (also in hundreds of milligrams). How much of each drug should be used if we want to minimize the duration of the infection. Justify that your answer is at least a local minimum' Problem 5. A company is planning to introduce two new products. . It costs $10 per unit to manufacture the first product and $30 per unit to manufacture the second product. . It is estimated that if the first product is priced at p1 dollars per unit and the second at p2 dollars per unit then q1 = 40 - 8p1 + 5p2 consumers will buy the first product and q2 = 50 + 9p1 - 7p2 will buy the second product. (a) Assuming the company only makes what it can sell, find the profit of the company as a function of p1 and p2. Hint: The revenue of the company is pig1 + P292 and the cost is 10q1 + 30q2. (b) How should the company price the two products to generate the largest possible profit? Show your answer corresponds to at least a local maximum