A farmer wants to allocate between 10 and 60% of his available acreage to each of corn, soybeans, and sunflowers. With markets varying wildly from year to year, he has done some research on past performance to guide his decisions. The following table shows the average return per acre and the covariances among categories that he has computed.

Corn Soybeans Sunflow Dollar return 77.38 88.38 107.50 Covariance Corn 1.09 -1.12 -3.15 Soybeans -1.12 1.52 4.38 Sunflow -3.15 4.38 12.95 The farmer wants the least risk plan that will average at least $90 per acre.

(a) Formulate this portfolio problem as a constrained NLP.

(b) Use class optimization software to start from a feasible solution and compute at least a local optimum.