The question refers to the following optimization problem: Maximize {z=f(x,y)= 2×x+3×y}, subject to ϕ(x,y)=√x+√y=5 Assume that the domain of both the objective function and the constraining function i

The question refers to the following optimization problem:

Maximize {z=f(x,y)= 2×x+3×y},

subject to ϕ(x,y)=√x+√y=5

Assume that the domain of both the objective function and the constraining function is the non-negative quadrant, that is,

Non-negative quadrant= {(x,y)∈R^2:x≥0,y≥0}

The graphical representation of the constraint can be seen in Figure 1. The equation of the tangent line at the point (9,4) is 2×x+3×y=30.

Figure 1

The optimization problem has been given to an economist and a mathematician. The economist claims that the problem has no solution and the mathematician asserts that there is a unique solution to the problem.

a.     Solve the optimization problem using the step-by-step procedure

b.    Who is right, the economist or the mathematician? To gain a positive mark you must justify your answer.