please help me tutor. i will provide the example on how to amswer the task. i hope you can help me by constructing an amswer based on the example. thank you.

Example 1: The sum of two positive numbers is 12. What are these numbers if their product is a maximum? Solution: Let x - one of the two positive numbers y- the other positive number x+y = 12 - This is the constraint. P = xy - This is the optimization equation Solve for one of the variables in the constraint. Then, substitute the value of this variable in the optimization equation. xty = 12 - constraint godmun ovilay = 12 - x meldong ort eased .01- biopovid P = xy - optimization equation = x (12 - x) = 12x - x2Find the first derivative. P = 12x - x2 P' = 12 - 2x Set the first derivative equal to zero. 12 - 2x = 0 -2x = -12 x = 6 Test: P' = 12 - 2x P" = -2 (negative) P" 0 The minimum value occurs when x = 10. 100 y = X 100 = 10 al conel off pnibling = 10 - the other number The two positive numbers are 10 and 10. om prionet to arefeltExample 5: An open box is to be made from a 24 cm cardboard by cutting equal squares out of the corners and turning up the sides. Find the height if the box that will give a maximum volume. Solution: 24x - 2x 24x - 2x 24x - 2x 24x - 2x Let x- height 24 - 2x - base V = lwh = (24 - 2x) (24 - 2x) (x) = (576 - 96x + 4x2) x = 576x - 96x2 + 4x3 = 4x3 - 96x2 +576x = x3 - 24x2 + 144x V' = 3x2 - 48x + 144 = x2 - 16x + 48 Equate the first derivative to 0. x2 - 16x + 48 = 0 (x - 12) (x - 4) = 0 x - 12 = 0 x - 4= 0 x = 12 x =4 Disregard x = 12 because x cannot be equal to 12. Test: V' = x2 - 16x + 48 V" = 2x -16 = 2(4) -16 = -8 - negative V"