Maali wants to open a business that manufactures speakers and subwoofers for car audio. After researching the topic, she estimates that if her company would make thousand subwoofers and thousand speakers per month, their revenue and cost functions in thousands of dollars would be: (, ) = (110 4.5) + (155 2) (, ) = 3 2 + 3 2 + 5 5 + 50 How many subwoofers and speakers should his potential new company manufacture each month in order to maximize their profit? What is the resulting maximum profit? What does your answer tell you about Maali's potential business?

Use the method of Lagrange Multipliers to find the maximum of (, ) subject to the given constraint. (, ) = 48 + 96 2 2 9 2 Constraint: 20 + 4 = 216