MATH 105 Lecture 18: MATH 105 Lecture 18
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Find two positive numbers whose sum is 300 and whose product is a maximum. The first step is to write down equations describing this situation. Let"s call the two numbers x and y and we are told that the sum is 300 (this is the constraint for the problem) or x+y=300. We are being asked to maximize the product: The next step is to determine the critical points for this equation. Just because we got a single value we can"t just assume that this will give a maximum product. We need to do a quick check to see if it does give a maximum. In this case we can quickly see that, We already have x so we need to determine y and that is easy to do from the constraint. y=300 150=150. Let x and y be two positive numbers such that x+2y=50 and (x+1)(y+2) is a maximum.
