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MATH SOLVE
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Find two numbers whose sum is 23 and whose product is a maximum.
4 months ago
Q:
Find two numbers whose sum is 23 and whose product is a maximum.
Accepted Solution
A:
Let x = the first numberLet y = the second number x + y = 23 eq1 y = 23- x
xy = Product eq2
Substitute eq1 into eq2. Lets get eq2 in terms of x.
Product = x(23 - x)Product = - x2 + 23x
we must find the vertex has coordinate (h, k). h = -b / 2a where:a = -1b = 23
h= -23 / -2 = 11.5
x = 11.5
Substitute this value of x into eq1 to find y. y = 23 - xy = 23 - 11.5y = 11.5
The two numbers that will give the largest product possible are 11.5 and 11.5.