Stock in Company A sells for $$86$ a share and has a $3-$year average annual return of $$25$ a share. The beta value is $1\mathrm{.}21.$ Stock in Company B sells for $$82$ a share and has a $3-$year average annual return of $$18$ a share. The beta value is $107.$ Derek wants to spend no more than $$17,000$ investing in these two stocks, but he wants to earn at least $$2100$ 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.

$|z||=$

subject $to86a+82b$

$25a+18b$

$a0,b0.$

$($Use integers or decimals for any numbers in the expressions. Do not include the $ symbol in your answers.$)$