Varma Investment Services must develop an investment portfolio for a new client. As an initial investment strategy, the new client would like to restrict the portfolio to a mix of two stocks.

Stock	Price/Share ($)	Estimated Annual Return (%)
AGA Products 1	50	6
Key Oil2	100	10

The client wants to invest $48,000 and established the following two investment goals.

Priority Level 1 Goal

Goal 1: Obtain an annual return of at least 9%.

Priority Level 2 Goal

Goal 2: Limit the investment in Key Oil, the riskier investment, to no more than 60% of the total investment.

(a)

Formulate a goal programming model for the Varma Investment problem. (Let x_i be the number of shares of stock i purchased, d_{p i} be the deviation variable which exceeds the value of goal i, d_{n i} be the deviation variable which is less than the value of goal i, for i = 1, 2.)

The client wants to invest $48,000 and established the following two investment goals. Priority Level 1 Goal Goal 1: Obtain an annual return of at least 9%. Priority Level 2 Goal Goal 2: Limit the investment in Key Oil, the riskier investment, to no more than 60% of the total investment. (a) Formulate a goal programming model for the Varma Investment problem. (Let xi be the number of shares of stock i purchased, dpi be the deviation variable which exceeds the value of goal i,dni be the deviation variable which is less than the value of goal i, for i=1,2.) MinP1(+P2(s.t. Funds Available P1GoalP2Goalxi,dnidpi0fori=1,2 (b) Use the graphical goal programming procedure to obtain a solution. (x1,x2)=(