I partly correct, check the incorrect block. Problem 14-02 (Algorithmic) Service
ID: 369596 • Letter: I
Question
I partly correct, check the incorrect block.
Problem 14-02 (Algorithmic) Services must develop an investment portfolio for a new dient. As an intial investment strategy, the new client would like to restrict the portfolio to a mix of two stocks: Estimated Annual Return (%) 6 Stock AGA Products Key Oil Price/Share s0 100 10 The client wants to invest $40,000 and established the following two investment goals Priority Level 1 Goal Goal 1: Obtain an annual return of at least 996. 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 DJS Investment problem. If you don't need the variable in the model, enter O". If you need a negative number, enter minus sign with it. Let = number of shares of AGA Products purchased x2-number of shares of Key Oil purchased Previous Check My Work 1 more Check My Work uses remaning Priority Level 2 Goal Goal 2: umit 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 DJS Investment problem. If you don't need the variable in the model, enter o. If you need a negative number, enter minus sign with it. Let x1-number of shares of AGA Products purchased x2 number of shares of Key Oil purchased 1P2(d2) 50 X1 100 X2 0.1 x x2 0.4 xX2 40000 | |-d11-10.09(x1+x21 x 1 Goal 0 x P2 Goal 0.06 x x1 0.6 x x1 b. Use the graphical goal programming procedure to obtain a solution x2 x2 Check My WorkExplanation / Answer
The correct LP model is as follows
a single unit deviation in P1 goal is equivalent to 25 unit deviation in P2 goal. Therefore, P1 index is 25 times that of P2.
Objective: Max 25*P1(d1-) + 1*P2(d2+)
50*x1 + 100*x2 <= 40000
P1 goal 50*.06*x1 + 100*0.1*x2 - d1+ + d1- = 50*.09*x1 + 100*.09*x2 this can be simplified as
or, 3*x1 + 10*x2 - d1+ + d1- = 4.5*x1 + 9*x2 bring x1 and x2 terms on the left hand side of the equation
or, -1.5*x1 + 1*x2 - d1+ + d1- = 0
P2 goal 100*x2 - d2+ + d2- = 50*.60*x1 + 100*.60*x2 this can be simplified as
or, 100*x2 - d2+ + d2- = 30*x1 + 60*x2 bring x1 and x2 terms on the left hand side of the equation
or, -30*x1 + 40*x2 - d2+ + d2- = 0
x1, x2, d1+, d1-, d2+, d1- >= 0