# Optimization problem

1. Dec 10, 2005

### seiferseph

I'm having trouble with this problem, i can't identify what you are given, so I can't set up an equation to optimize. Thanks

2. Dec 10, 2005

### Staff: Mentor

Your objective function is yield(Ntrees). You have the constraint 0<Ntrees<=60. Oh, also, Ntrees is an integer.

-Dale

3. Dec 10, 2005

### seiferseph

the part i'm having trouble with is forming an equation

4. Dec 10, 2005

### cronxeh

I dont get it either.
Are you given 30 trees @ 50 Kg/tree = 1500 Kg yield as an initial condition? If the total yield increase of 7% from that is 1605 then the number of trees s around 33 (1600 kg total yield) to 34 (1632 kg total yield). Frankly this problem makes absolutely no sense. They are not hinting you will get more yield per tree if you planted less, so it must be just about setting up linear equation and solving it
30 trees * 50 Kg/tree = 1500 Kg yield
Y = Yield/tree (x trees) = -0.5*x + 65
Max yield = Y*x = -0.5x^2 + 65x
Max yield increase of 7% = 1605 = -0.5x^2 + 65x

Last edited: Aug 21, 2010
5. Dec 10, 2005

### Staff: Mentor

I think the 7% is not part of the question. I think it may be e.g. the number of points it is worth on the test or assignment.

Your "max yield" equation is the correct objective function. Just maximize it subject to the constraints (0<x<=60 and x is an integer).

-Dale

6. Dec 10, 2005

### seiferseph

solving that gets critical pt of 65, right? which is outside the domain. so do i just take the endpoint where x = 60

7. Dec 10, 2005

### cronxeh

You dont have enough information to conclude that. There is no data on just how much the disease affects the yield. There is no data on the yield amounts between 1 to 30 - is it 50 kg/tree? Is it much more?

So the only definitive conclusion you can draw, whatever that means for this problem, is that from 30 to 60 trees the most optimal and maximum yield is at 60 trees. Clearly this is not an optimization problem because 0.5 kg decrease is so insignificant to even make a difference. If it was 1 kg/tree decrease then this will be an optimization problem.

Last edited: Dec 10, 2005
8. Dec 10, 2005

### Staff: Mentor

Constrained optimization problems often give optimal results determined by the constraints rather than the objective function.

In any case, yes, whenever your objective function is strictly increasing over the entire feasible range then the maximum will be at the "upper" constraint.

-Dale