A stockbroker, Richard Smith, has just received a call from his most important client, AnnHardy. Ann has $50,000 to invest and wants to use it to purchase two stocks. Stock 1 is asolid blue-chip security with a respectable growth potential and little risk involved. Stock 2 ismuch more speculative. It is being touted in two investment newsletters as havingoutstanding growth potential, but also is considered very risky. Ann would like a largereturn on her investment, but also has considerable aversion to risk. Therefore, she hasinstructed Richard to analyze what mix of investments in the two stocks would beappropriate for her. Ann is used to tailing in units of thousands of dollars and 1,000-share blocks of stocks. Using these units, the price per block is 20 for stock 1 and 30 for stock 2. After doing some re- search, Richard has made the following estimates. The expected return per block is 5 for stock 1 and 10 for stock 2. The variance of the return on each block is 4 for stock 1 and 100 for stock 2. The covariance of the return on one block each of the two stocks is 5.

Required:
Without yet assigning a specific numerical value to the minimum acceptable expected return, formulate a nonlinear programming model for this problem.