Question $3$

$20$ points

VanMetals has $$3500$ available for the production of new products. Wall Inc. will buy all the products they can produce.

After an initial screening, VanMetals reduced the production alternatives to tables and chairs. Each table can be produced with a cost of $$400.$ Each chair can be produced for $$350.$

VanMetals can devote up to $100$ hours to these new products; each table is expected to require $16$ hours, and each chair is expected to require $8$ hours. The selling prices are $$600$ per table and $$400$ per chair.

VanMetals$$s owner would like to use all$-$integer linear programming without relaxation to determine the number of tables and the number of chairs to produce to maximize revenue.

What are the decision variables? $(2$ points$)$

What is the objective function for revenue? $(3$ points$)$

What are the constraints? $(4$ points$)$

What is the number of tables and the number of chairs to be produced to maximize revenue? $(4$ points$)$

What is the Maximum revenue they can expect? $(3$ points$)$

Draw the graphical solution of the all$-$integer problem. $(4$ points$)$

take a picture of all your work and upload the files. $($You can use Excel Solver$)$