Each coffeetable produced by Robert West Designers nets the firm a profit of$15. Each bookcase yields a $12 profit. West's firm is smalland its resources limited. During any given production period (of 1week), 10 gallons of varnish and 12 lengths of high-quality redwoodare available. Each coffee table requires approximately 1 gallon ofvarnish and 1 length of redwood. Each bookcase takes 1 gallon ofvarnish and 2 lengths of wood. Formulate West'sproduction-mix decision as a linear programming problem, and solve.
(a) How many tablesshould be produced each week?
(b) How many bookcases should be produced each week?
(c) What will themaximum profit be?