Sketch the region that corresponds to the given inequalities, say whether the region is bounded or unbounded, and find the coordinates of all the corner points (if any). Make sure you use a test point in your work. Shade the region(a) that is NOT the solution and label the region SOLUTION SET. 30x+20y>=600 10x+40y>=400 20x+30y>=600 x>=0, y>=0

A piece of string whose length is given below is cut into two pieces. One piece is used to form an equilateral triangle and the other to form a circle. What should be the perimeter of the equilateral triangle and the circumference of the circle so that the sum of the areas is a minimum? Find the minimum sum of the areas. Express your answer in terms of T. The length of string is 64 cm.

6. Cost A farmer wishes to enclose a rectangular field of area 450 square feet using an existing wall as one of the sides. The cost of the fence for the other three sides is $3 per foot. Find the dimensions of the rectangular field that minimizes the cost of the fence.