Each coffee table produced by Robert West Designers nets the firm aprofit of $16. Each bookcase yields a $12 profit. West's firmis small and its resources limited. During any given productionperiod (of 1 week), 10 gallons of varnish and 12 lengths ofhigh-quality redwood are available. Each coffee table requiresapproximately 1 gallon of varnish and 1 length of redwood. Eachbookcase takes 1 gallon of varnish and 2 lengths of wood. FormulateWest's production-mix decision as a linear programming problem, and solve.
(a) How many tables should be produced each week?
(b) How many bookcases should be produced each week?
(c) What will the maximum profit be?