A craftsman named William Barnes builds two kinds of

birdhouses, one for wrens and a second for bluebirds. Each wren birdhouse takes $4$ hours of labor and $4$ units of lumber. Each

bluebird house requires $2$ hours of labor and $12$ units of lumber. The craftsman has available $60$ hours of labor and $120$ units of

lumber. Wren houses yield a profit of $$6$ each and bluebird houses yield a profit of $$15$ each.

The aim of the objective function for William should be to

the objective value.

Decision variables:

$x=$ number of wren houses to be produced

$Y=$ number of bluebird houses to be produced

a$)$ Objective function:

$Z=x+Y$

Subject to:

$4x+2Y,$gradx$60,(C_1)$

$4x+12Y,120,(C_2)$

$x,Y0,$

b$)$ On the graph on right, constraints $C_1$ and $C_2$ have been plotted.

Using the point drawing tool, plot all the corner points for the feasible area.

The optimum solution is:

$x=(round$ your response $to$ two decimal places$).$

$Y=(round$ your response $to$ two decimal places$).$

Optimal solution value $\text{'}\text{'}$Z$\text{'}=($round your response to two decimal places$).$