Each coffee table produced by Kevin Watson Designers nets the firm a profit of $9. Each bookcase yields a $12 profit. Watson's form is small and its resources limited. During any given production period (of 1 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 Watson's production-mix decision as a linear programming problem, and solve. How many tables and bookcases should be produced each week? What will the maximum profit be?

b) If the profit for the coffee table is increased from $ 9 to $ 15, what is the new optimal solution?

c) If the lengths of high-quality redwood are increased from 12 to 16, what is the new optimal solution?

Show all working out