3. Each coffee table produced by Meising Designers nets the firm a profit of $9. Each bookcase yields a $12 profit. Meisings firm is small, and its resources are limited. During any given production period of one 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.

a) Formulate Meisings production mix decision as a LP problem. Solve for the optimal solution using simplex method

b) In the second simplex table, comment and analyze the coefficients (substitution rates) of each variable columns

c) How many unused resources are remained with your final answer

d) Convert the primal problem in dual form and solve it using simplex method

e) Compare the results you find in a) and d)