Can a calculator solve stuff like this:
Of all numbers that add to 52, find the pair that has the maximum product.
That is, maximize the objective function Q = xy subject to the constraint x + y = 52.
The answer is x = 26, and y = 26.
Yes, a calculator can solve this problem by finding the maximum value of the product function Q = xy subject to the constraint x + y = 52 using methods such as differentiation or optimization algorithms. Alternatively, the calculator can generate a table or graph of the product function over a range of values of x and y that add up to 52, and then identify the maximum value and corresponding values of x and y.
it is helpful to remember that for a given sum, the maximum product is (sum/2)^2
Similarly, for a given quadriltateral perimeter, a square provides maximum area.
For a given area, a square provides minimum perimeter.