Stock in Company A sells for $$92$ a share and has a $3-$year average annual return of $$21$ a share. The beta value is $1\mathrm{.}26.$ Stock in Company B sells for $$84$ a share and has a $3-$year average annual return of $$15$ a share. The beta value is $1\mathrm{.}13.$ Derek wants to spend no more than $$16,000$ investing in these two stocks, but he wants to earn at least $$2200$ 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 to

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$]$

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