To find:Twonumbers whose sum is given and product is maximum.
![Check Mark](/static/check-mark.png)
Answer to Problem 55E
The product of two numbers whose sum is 110, is maximum when they are 55 and 55
Explanation of Solution
Given data:
The sum of two numbers is 110.
Concept used:
The vertex of downwards opening quadratic function is
Calculations:
Let x and z be two numbers whose sum is 110 and product is maximum. We denote the product of numbers by y. Thus,
From results (1) and (2), we have
As
Now we obtain standard form of quadratic function
We know the vertex of quadratic function (parabola)
That shows, the product
Thus, the product of two numbers whose sum is 110, is maximum when they are 55 and 55.
Conclusion:
The product of two numbers whose sum is 110, is maximum when they are 55 and 55.
Chapter 2 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
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