LP$\mathrm{.}02$ Each coffee table produced by Kevin Watson Designers nets the firm a profit of $9$ dollars. Each bookcase yields $11$ dollars profit. Watson's firm is small and its resources limited$.$ During any given production period $($of $1$ week$),8$ gallons of varnish and $14$ lengths of high$-$quality redwood are available. Each coffee table requires approximately $2\mathrm{.}5$ gallons of varnish and $2\mathrm{.}5$ lengths of redwood. Each bookcase requires $0\mathrm{.}5$ gallons of varnish and $3\mathrm{.}5$ lengths of wood.

Formulate Watson's production$-$mix decision as a linear programming problem and solve. How many tables and bookcases should be produced each week?

Tables:

Preview $($round to two decimal points$)$

Bookcases:

Preview $($round to two decimal points$)$

What will the maximum profit be$?$

Preview $($round to two decimal points$)$

Which of the constraints are binding?

Varnish

Wood

What are the shadow prices for?

Varnish:

Preview $($round to two decimal points$)$

Wood:

Preview $($round to two decimal points$)$