A farmer needs to enclose by fences a rectangular field containing 75,000 square feet. One side of the field lies along a river and one side lies along a road. The river is perpendicular to the road. He needs a more expensive fence on the sides next to the road and the river, with a cheaper fence being used on the remaining 2 sides. The fence costs $20 per foot along the road, $15 per foot along the river, and $10 per foot on the remaining 2 sides to be fenced. Find the dimensions he should use for the field to fulfill the above criteria and minimize the cost of fencing the field. Also calculate the minimum cost possible for constructing a field that meets the above criteria? INCLUDE A DIAGRAM OF THE FIELD AS PART OF YOUR WORK AND SHOW ALL THE WORK. Find what the side next to the road must equal. Find what the side next to the river must equal. And find the minimum cost of the fence.