What is the maximum product of two numbers whose sum is 22? What numbers yield this product?
Well, to find the maximum product of two numbers whose sum is 22, we need to do a little bit of math. Let's suppose the two numbers are x and y. We know that x + y = 22.
Now, let's think about maximizing the product. If we want the product of x and y to be as large as possible, we want the two numbers to be as close as possible. Just think of them as a pair of inseparable best buddies.
So, let's split 22 into two equal halves: 11 and 11.
Therefore, the maximum product of two numbers whose sum is 22 is 11 * 11, which equals 121.
In conclusion, the numbers that yield this product are 11 and 11. They're truly a dynamic duo, inseparable and multiplying their way to 121!
To find the maximum product of two numbers whose sum is 22, we can use the concept of maximizing a product when numbers are evenly distributed.
Let's assume the two numbers are x and y.
Given that the sum of x and y is 22, we can set up the equation:
x + y = 22
To maximize the product, we need to distribute the numbers as evenly as possible. In other words, we need to find two numbers that are as close as possible to each other.
Since the sum is 22, two numbers that are closest to each other would be 11 and 11. Therefore, the numbers that yield the maximum product are 11 and 11.
Product of 11 and 11 = 11 * 11 = 121
Thus, the maximum product is 121, and the numbers that yield this product are 11 and 11.
To find the maximum product of two numbers whose sum is 22, we can use the concept of optimization. Let's denote the two numbers as x and y. The sum of x and y is given as 22, which translates to the equation x + y = 22. We want to maximize the product xy.
To solve this problem, we'll use the technique of algebraic optimization. We can rewrite the equation x + y = 22 as y = 22 - x. Substituting this value of y into the expression for the product, we get:
Product = x * (22 - x)
This is now a function of a single variable, x. To find the maximum product, we need to find the value of x that maximizes this function.
To maximize the product, we can take the derivative of the function with respect to x and set it equal to zero. Let's differentiate the function:
d(Product)/dx = 22 - 2x
Setting the derivative equal to zero:
22 - 2x = 0
2x = 22
x = 11
Now that we know x = 11, we can substitute it back into the equation y = 22 - x to find y:
y = 22 - 11
y = 11
Therefore, the maximum product of two numbers whose sum is 22 is achieved when x = 11 and y = 11. The numbers that yield this product are 11 and 11.