Multivariable Linear Programming Problem using linprog() Function (please help)

I am trying to optimize a multivariable optimization problem using the linprog() Function in Matlab. Please refer to the attached photo for more details. In the problem it says to convert the nonlinear problem into a linear problem and then use the linprog function to calculate the x and y value of a rectangle shape. My attempt at this is follows.

P = 2x + 2y = 100 => P = x + y = 50 (Constraint Function)

A = xy (maximize this)

In order to use the Linprog function I first need to convert the nonlinear equation into a linear equation using Taylor Series:

L(x,y) = A(a,b) + df/dx(a,b)(x-a) + df/dy(a,b)(y-b)

Now, according to the linprog() function i need to determine f, A, b, Aeq, beq, lb, ub

f = ???

A = [1 1]

b = [50]

Aeq = []

beq = []

lb = [0 0]

ub = []

My question is that what do i input for f?