optimization and sensitivity analysis

Hi. Here are my objectives:

1. I want to find what are the value of "pa" and "pb" that maximize the equation: pi= (pa+pb)*na*nb, where "na" is a function of "pa", "nb" is a function of "pb".
2. And I want to know how the optimal combination of pa,pb) changes with the parameter "ba" and "bb", and
3. to draw a graph with "x=ba, y=bb, z =pa" as well as a graph "x=ba, y=bb, z =pb".

Could you please help me with the code? Thanks a lot.

Parameters

ba >=0 <=8

bb >=0 <=10

Variables

pa=0

pb=0

Equations

maximize (pa+pb)*na*nb

va=rand(1000,1)*ba;
vb=rand(1000,1)*bb;

na=0;
for i=1:size(va,1)
    if va(i,1)>pa
        na=na+1;
    end
end

nb=0;
for i=1:size(vb,1)
    if va(i,1)>pb
        nb=nb+1;
    end
end

Answer 1

[Kartik Saxena]

Hi,

To find the values of 'pa' and 'pb' that maximize the equation "pi = (pa + pb) * na * nb", where 'na' is a function of 'pa' and 'nb' is a function of 'pb', and to understand how the optimal combination changes with parameters 'ba' and 'bb', you can use MATLAB's Global Optimization Toolbox.

All of these objectives can be achieved by using this toolbox along with functions like 'plot' and 'surf', which would eliminate the need for redundant code as well.

Refer to the following MathWorks documentation for detailed information regarding Global Optimization Toolbox:

https://www.mathworks.com/help/gads/index.html?s_tid=CRUX_lftnav