Final answer:
To find three positive numbers whose sum is 220 and whose product is a maximum, we can use a trial-and-error method. Start by choosing two numbers, x and y, and solve for the third number. Express the product of the three numbers as P = x * y * (220 - x - y). Take the derivative of P with respect to x, set it equal to zero, and solve for x.
Step-by-step explanation:
To find three positive numbers whose sum is 220 and whose product is a maximum, we can start by using a trial-and-error method. We need to find three numbers that add up to 220, so let's start with two numbers and subtract them from 220 to find the third number.
For example, if we choose two numbers, x and y, we can write the equation x + y + z = 220, where z is the third number. Solving for z, we get z = 220 - x - y.
Next, we can express the product of the three numbers, P, as P = x * y * z = x * y * (220 - x - y). To find the maximum product, we can take the derivative of P with respect to x, set it equal to zero, and solve for x.
By repeating this process for different values of x and y, we can find the three positive numbers that maximize the product.