Let the person takes x tablets of type X and Y tablets of type Y.

According to the given conditions, we have

The shaded region AGHF represents the feasible region of the given LPP. The corner points of the feasible region are A(0, 9), G(1,, 9), H(6, 1) and F(8, 0). The values of the objective function at these points are given in the following table :