Each coffee table produced by Kevin Watson Designers nets the firm a profit of $ $10.$ Each bookcase yields a $ $15$ profit.$$ Watson's firm is small and its resources limited$.$ During any given production period $($of $1$week$),8$ gallons of varnish and $12$ lengths of$$ 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

$$

Minimize

Maximize

the objective value.

Decision$$ variables:

X$=$ number of coffee tables produced$/$ week

Y$=$ number of bookcases produced$/$ week

Objective$$ function:

Zequals

$$

enter your response hereXplus

$$

enter your response hereY

Subject$$ to:

$1$Xplus$1$Y

$$

greater than or equals

less than or equals

$8$

$($Upper C $1)$

$1$Xplus$2$Y

$$

greater than or equals

less than or equals

$12$

$($Upper C $2)$

$$X$,$ Y greater than or equals$0$

The optimum solution$$ is:

X$=$

$$

enter your response here $($round your response to two decimal$$ places$).$

Y$=$

$$

enter your response here $($round your response to two decimal$$ places$).$

Optimal solution value Z $=$

$$

enter your response here $($round your response to two decimal$$ places$).$

$.$

$.$

$.$