Each coffee table produced by Kevin Watson Designers nets the firm a profit of $$10.$ Each bookcase yields a $$15$ profit. Watson's firm is small and its resources limited$.$ During any given production period $($of $1$ week$),10$ gallons of varnish and $12$ lengths of high$-$quality redwood are available. Each coffee table requires approximately $1$ gallon of varnish and $1$ length of redwood. Each bookcase takes $1$ gallon of varnish and $2$ lengths of wood. The firm wants to maximize its profit by deciding the number of coffee tables and the number of bookcases produced each week, using a linear programing problem.

The aim of the objective function for Kevin should be to Maximize the objective value.

Decision variables:

$x=$ number of coffee tables produced $\frac{?}{?}$ week

$Y=$ number of bookcases produced $\frac{?}{?}$ week

Objective function:

$Z=10x+15Y$

Subject to:

$[$

$]$

The optimum solution is:

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

$Y=3($round your response to two decimal places$).$

Optimal solution value $Z=($round your response to two decimal places$)$