A data scientist is in charge of developing the Weekly Production Plan for two

key products that the furniture factory makes: chairs and tables. The data scientist,

using machine learning techniques, predicts that the selling price of a chair is $$45$

and the selling price of a table is $$80$ dollars. There are two critical resources in

the production of chairs and tables: Mahogany $($measured in board square$-$feet$)$

and labor $($measured in work hours$).$ There are $400$ units of mahogany available

at the beginning of each week. There are $450$ units of labor available during each

week. The data scientist estimates that One chair requires $5$ units of mahogany

and $10$ units of labor. One table requires $20$ units of mahogany and $15$ units of

labor. The marketing department has told the data scientist that ALL the

production chairs and tables can be sold. How many chairs and tables must they

produce to maximize the total revenue?

$$ Formulate a model to help the data scientists make a Production Plan

that maximizes total revenue.

$$ Suppose the labor capacity is increased from $450$ to $451$ hours. What is

the increase in the objective function value from such an increase?

$$ Suppose the mahogany capacity is increased from $400$ to $401$ hours.

What is the increase in the objective function value from such an

increase?

$$ is it profitable to make a third product, like desks? Assume that the desk

is priced at $$110$ and that it consumes $15$ units of mahogany and $25$ units

of labor.