python 3.5 or later please!

Objective: To write and run a python program to solve an integer programming problem. Problem: Let f(x,y) (x - 1)2 -4* (x-1) (y -3) +5 (y -3)2 - 841 The equation f(x,y) 0 defines an ellipse in the xy-plane. Let C denote the convex region in the xy-plane defined by f(x,y) s 0. The boundary of C is the ellipse f(x,y) 0 itself. The lattice points in the xy-plane are those ordered pairs (x, y) for which both x and y are integers. This problem is concerned with finding extremal lattice points in C, and extremal lattice points on the boundary of C. Write a python program that does all of the following: (1) Count the number of lattice points inC. (2) Count the number of lattice points on the boundary (3) Locate the minimum x value for all lattice points in C. (4) Locate the maximum x value for all lattice points in C. (5) Locate the minimum y value for all lattice points in C. (6) Locate the maximum y value for all lattice points in C. (7) Locate the lattice point in C closest to the origin. (8) Locate the lattice point in C farthest from the origin. (9) Locate the lattice point on the boundary of C closest to the origin. (10) Locate the lattice point on the boundary of C farthest from the origirn. Objective: To write and run a python program to solve an integer programming problem. Problem: Let f(x,y) (x - 1)2 -4* (x-1) (y -3) +5 (y -3)2 - 841 The equation f(x,y) 0 defines an ellipse in the xy-plane. Let C denote the convex region in the xy-plane defined by f(x,y) s 0. The boundary of C is the ellipse f(x,y) 0 itself. The lattice points in the xy-plane are those ordered pairs (x, y) for which both x and y are integers. This problem is concerned with finding extremal lattice points in C, and extremal lattice points on the boundary of C. Write a python program that does all of the following: (1) Count the number of lattice points inC. (2) Count the number of lattice points on the boundary (3) Locate the minimum x value for all lattice points in C. (4) Locate the maximum x value for all lattice points in C. (5) Locate the minimum y value for all lattice points in C. (6) Locate the maximum y value for all lattice points in C. (7) Locate the lattice point in C closest to the origin. (8) Locate the lattice point in C farthest from the origin. (9) Locate the lattice point on the boundary of C closest to the origin. (10) Locate the lattice point on the boundary of C farthest from the origirn