Question

HuileWUIR. HVVHO SECUIT 1.5 9 of 10 (6 complete) HW Score: 36.25%, 3.63 of 10 pts Score: 0.38 of 1 pt 7.3.23-BE Question Help Stock in Company A sets for 589 a share and has a 3-year average annual return of $25 a share. The beta value is 104. Stock in Company B ses for 586 a share and has a 3-year average annual return of 516 a share. The beta value is 1.19. Derek wants to spend no more than $14,000 investing in these two stocks, but he wants to earn at least 52200 in annual revenue. Derek also wants to minimize the risk Determine the number of shares of each stock that Derek should buy Set up the linear programming problem. Let a represent the number of shares of stock in Company Ab represent the number of shares of stock in Company B, and z represent the total beta value Minimize 2= 1,04a.1.19 subject to 89-86b514000 25a 1662 2200 00 (Use integers of decimals for any numbers in the expressions. Do not include the symbol in your answers) Derek should buy share(s) of stock in Company A and share(s) of stock in Company B. (Round to the nearest integer as needed) Pets TO

Answer 1

Let 'a' and 'b' be the number of shares of Company-A and Company-B bought respectively for optimal risk.

Minimize Z = overall beta = 1.04 a + 1.19 b

Subject to,

89 a + 86 b <= 14000 (budget constraint)

25 a + 16 b >= 2200 (minimum revenue)

a, b >= 0

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LINDO Code:

Min 1.04 a + 1.19 b
s.t.
89 a + 86 b < 14000
25 a + 16 b > 2200
end

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Solution:

Global optimal solution found. Objective value: Infeasibilities: Total solver iterations: Elapsed runtime seconds : 91.52000 0.000000 1.31 Model Class : Total variables: Nonlinear variables: Integer variables: OON Total constraints: Nonlinear constraints: O Total nonzeros: Nonlinear nonzeros: O O Variable Value 88.00000 0.000000 Reduced Cost 0.000000 0.5244000 Slack or Surplus 91.52000 6168.000 0.000000 45200 Dual Price -1.000000 0.000000 -0.4160000E-01 000

So,

Buy 88 shares of stock-A and 0 shares of stock-B to be bought.