SOLUTION: Find a pair of numbers with a sum of 26 and a product that is a maximum. Find the maximum product.

Question 511607: Find a pair of numbers with a sum of 26 and a product that is a maximum. Find the maximum product.
Answer by oberobic(2304) (Show Source): 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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