You can put this solution on YOUR website! x + y = 26
so
x = 26-y
.
The product is
z = x * y = (26-y) * y
.
z = 26y -y^2
.
To find the maximum, take the first derivative and solve it.
.
dz/dy = 26 - 2y
.
26-2y = 0
26 = 2y
y = 13
.
Check:
y
x=26-y
x*y
13
13
169
12
14
168
11
15
165
10
16
160
9
17
153
8
18
144
7
19
133
6
20
120
5
21
105
4
22
88
3
23
69
2
24
48
1
25
25
.
Answer: The pair of numbers are 13 and 13 that total 26 and maximizes the product.
.
Done.
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