Stock in Company A sells for $86 a share and has a 3-year average annual return of $22 a share. The beta value is 1.03. Stock in Company B sells for $85 a share and has a 3-year average annual return of $17 a share. The beta value is 1.21. Derek wants to spend no more than $18,000 investing in these two stocks, but he wants to earn at least $2900 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 A, b represent the number of shares of stock in Company B, and z represent the total beta value
subject to $86a + 85b$
$22a + 17b$
$a \ge 0, b \ge 0$
(Use integers or decimals for any numbers in the expressions. Do not include the $ symbol in your answers.)