1. (Maximizing yield) An apple orchard has an average yield of 36 bushels of apples/tree if tree density is 22 trees/acre. For each unit increase in tree density, the yield decreases by 2 bushels/tree. How many trees should be planted in order to maximize the yield? 2. (Minimizing packaging costs) A rectangular box is to have a square base and a volume of 40 ft. If the material for the base costs 0.3 $/square foot, the material for the sides costs 0.1$/square foot, and the material for the top costs 0.2$/square foot, determine the dimensions of the box that can be constructed at minimum cost. 3. A grain silo has the shape of a right circular cylinder surmounted by a hemisphere (see the accompa- nying figure). If the silo is to have a capacity of (504 ) ft, find the radius and height of the silo that requires the least amount of material to construct. (Hint: The volume of the silo is V = r h+r, and the surface area (including the floor) is S = 7(3r + 2rh)). 2 4. Find the indefinite integrals. h a) (2x-8) dx x-8x+16 b) | 2x dx (x+3) d) 77x+12 dx e) se 8x-20 dx c) 2.xex+5 dx f) / (ln x) X d.x