## taranicolee 3 years ago can someone explain to me how to find two positive numbers such that the sum of the first and twice the second is 100 and their product is a maximum

1. zordoloom

You still there? Do you need help?

2. taranicolee

3. zordoloom

Do you know calculus?

4. taranicolee

well haha i'm in the class right now but not really...

5. zordoloom

Okay. That's fine.

6. taranicolee

well are you going to help?(:

7. zordoloom

Do you want just the answer, or how to get the answer?

8. taranicolee

how to get it please (:

9. taranicolee

how to get it please (:

10. zordoloom

okay.

11. zordoloom

let x= the first number let y= the second number

12. zordoloom

so, x+2y=100.

13. zordoloom

You are trying to maximize the product yz. so let z= the product = to xy

14. zordoloom

Following so far?

15. taranicolee

yeah(:

16. zordoloom

okay, so solve x+2y=100 for x. x=100-2y z=xy z=(100-2y)y z=y(100-2y) z=100y-2y^2

17. zordoloom

Now, just find the vertex of that graph using -b/2a

18. zordoloom

Therefore, the first value is 25 and the second value is 50.

19. zordoloom

Let me simplify this down a bit, because I was writing out my work which may be a bit confusing.

20. zordoloom

So, you have been told that the sum of the first number, twice the second is 100 (I'll use just x and y this time to make things less confusing) so, x+2y=100.

21. zordoloom

You are trying to minimize the product, P=xy. So solve the first equation x+2y=100, for x.........x=100-2y. Now substitute this into the product formula ( P=xy)

22. taranicolee

ohhh wait i get it! thank you!!!! do you have time to help me with another one?(:

23. zordoloom

P = xy = (100 − 2y)y = 100y − 2y^2

24. zordoloom

Sure.