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Question:
Each coffee table produced by Robert West Designers nets the firm a profit of $9. Each bookcase yields a $12 profit. West's firm 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.
Formulate West'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?
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What is the optimal solution to this problem? Solve it graphically. If a technical breakthrough occurred that raised the profit per unit of x to $8 would this affect the optimal solution.
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