assume we havesive species which can be in one of three classes: infant, immuture, or mature. The dynamics of the species is governed by the equation $\displaystyle N_{t+1}$= L$\displaystyle N_{t}$

where $\displaystyle N_{t}$ is a vector of length 3 giving the area occupied by each class, and L is 3*3 matrix which specifies the fecundity and survival of the species in terms of spread.

Give perunit area costs $\displaystyle c_{k}$ of culling individuals of type k, we wish to determine the optimal amount of class k to remove at the end of each year t=1,2-we denote these variables $\displaystyle H_{k,t}$ in order to minimise the total area occupied by the invasive at the end of year 2.

Assume we have a maximum budget of $\displaystyle \$$C in each year

questionformulate this problem as a linear program

thanks in advance