Stock in Company A sells for $$87$ a share and has a $3-$year average annual return of $$24$ a share. The beta value is $1\mathrm{.}04.$ Stock in Company B sells

for $$83$ a share and has a $3-$year average annual return of $$19$ a share. The beta value is $1\mathrm{.}18.$ Derek wants to spend no more than $$17,000$

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.

$z=1\mathrm{.}04a+1\mathrm{.}18b$

$87a+83b17000$

$24a+19b2200$

$a0,b0.$

subject to

$87a+83b17000$

$24a+19b2200$

$a0,b0.$

$($Use integers or 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 $0$ share$($s$)$ of stock in Company B$.$

$($Round to the nearest integer as needed.$)$