The Kingdom of Quadra lives in the realm of xy-lia. You are a map maker from a foreign country tasked with drawing a map of Quadra. King Calcula will reward you based on the neatness and accuracy of your map. He has bad eyesight so please make a large drawing. You are given the following information:
(a) Quadra is 300km wide and 400km North to South. You may draw it with its center at the origin.
(b) The population density at a particular point (x, y) in Quadra is given by the function f(x, y) = x^3 - 30000x + y^3 - 30000y + 4000000 where x and y are km East and North of the origin respectively.
(c) The maximum population of Quadra occurs at its capital city, Vectoria.
(d) The minimum population of Quadra occurs at Nabla Bog.
(e) Quadra's population density has two saddle points, one at each of its major trading posts.
1. Draw Quadra and label its borders, capital, bog, and trading posts. Give the exact coordinates of each.