1. Each coffee table produced by John Alessi Designers nets the firm a profit of $9. Each bookcase yields a $12 profit. Alessi's firm is small and its resources 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. Formulate Alessi's production mix decision as a linear programming problem and solve, using the simplex method. How many tables and bookcases should be produced each week? What will the maximum profit be?
2. Set up a complete initial tableau for the data (repeated below) that were first presented in Solved Problem T3.1.
Minimize cost = 4X1 + 1X2 + 0S1 + 0S2 + MA1 + MA2
Subject to: 3X1 + 1X2 + 1A1 = 3 4X1 + 3X2 - 1S1 + 1A2 = 6 1X1 + 2X2 + 1S2 = 3
(a). Which variable will enter the solution next?
(b). Which variable will leave the solution?