investment advisors inc is a brokerage firm that maqnages stock portfolios for a number of clients. A particular portfolio consist of U shares of u.s oil and h shares of huber steel. the annual return is us oil is $3 per share and the annual return for huber steel is $5 per share. U.S oil sells for $25 a share and huber steel sells for $50 a share. The portfolio has $80,000 to be invested. The portfolio risk index (0.50 per share of U.S oil and 0.25 per share for huber steel) Has a max of 700. In addition, the portfolio is limited to a max of 1000 shares of u.s oil. The linear programming formulation that will maximize the total annual return of the portfolio is as follows.

max: 3U+ 5H Maximize total annual return
s.t.
25u + 50H <= 80,000 Funds avialable
0.50U + 0.25D <= 700 Risk maximum
1u <= 1000 U.S oil maximum
U,H => 0