Find two positive real numbers whose product is a maximum.

puntgewelb5 2021-11-11 Answered
Find two positive real numbers whose product is a maximum. The sum is 110.
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Expert Answer

Witionsion
Answered 2021-11-12 Author has 19 answers

Let x and y be the two positive real numbers. Write an equation to show that the sum of the two positive real numbers is 110.
x+y=110
Solve for the value of y.
x+y=110
x+yx=110x
y=110x
Write an equation to show that the product of the two real numbers is the maximum. Let f(x) be the maximum. Substitute the values of x and y. Write as a quadratic function, f(x)=ax2+bx+c
f(x)=xy
f(x)=x(110x)
f(x)=110xx2
f(x)=x2+110x
a=1 which is a<0, the maximum at x=b2a. Detemine the value of x. Let a=-1 b=110
x=b2a
x=1102(1)
x=1102
x=55
Substitute the value of x in y=110x
y=110x
y=11055
y=55
The two positive real numbers are 55 and 55

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