1. suppose that R = m+n and mn = 1000. Find the value of m that minimizes R, for R>0.

2. If K= pq and p-q = 1500 find the value of p that makes K a minimum.

3. If W=g^2h and g^2 +4gh=2700, find the value of h that maximizes W if g>0 and h>0.

4. A rectangular backyard playpen for a child is to be enclosed with 16 m of flexible fencing. What dimensions of the rectangle will provide the maximum area for the child to play?

5. A rectangular coral is to be enclosed along the side of a horse barn with the barn serving as one side of the corral. What dimensions of the corral using 40 m of fencing will enclose the maximum are for the horses?

6. A rectangular garden plot requires an area of 32 m^2 for the variety of vegetables that are to be planted. What dimensions of the plot will use the least amount of fencing to enclose the garden?