info372-hwk6-sol

info372-hwk6-sol - INFO 372 Homework 6 Due date Tuesday May...

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INFO 372 Homework 6 Due date: Tuesday, May 2, at the beginning of class. 1 - TOYS4U, Inc. manufactures two types of wooden toys: dinosaurs and tractors. A dinosaur sells for \$27 and uses \$10 worth of raw materials. Each dinosaur that is manufactured increases the company’s variable labor and overhead costs by \$14. A tractor sells for \$21 and uses \$9 worth of raw materials. Each tractor built increases the company’s variable labor and overhead costs by \$10. The manufacture of wooden dinosaurs and tractors requires two types of skilled labor: carpentry and finishing. A dinosaur requires 2 hours of finishing labor and 1 hour of carpentry labor. A tractor requires 1 hour of finishing and 1 hour of carpentry labor. Each week, TOYS4U can obtain all the needed raw material but only 100 finishing hours and 80 carpentry hours. Demand for tractors is unlimited, but at most 40 dinosaurs are bought each week. TOYS4U wants to maximize weekly profit (revenues – costs). a) Formulate a linear programming model of TOYS4U’s situation that can be used to maximize weekly profit. X1 number of dinosaurs produced each week X2 number of tractors produced each week dinosaurs tractors A Revenue \$27 \$21 B Cost Raw Material Labor + Overhead \$10 \$14 \$9 \$10 Profit (A-B) \$3 \$2 Resource Requirements dinosaurs tractors Availability Finishing Labor 2 hours 1 hour 100 hours Carpentry labor 1 hour 1 hour 80 hours Max Weekly Demand unlimited 40

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Max z = 3 x1 + 2 x2 Subject to: 2 x1 + x2 100 (finishing constraint) x1 + x2 80 (carpentry constraint) x1 40 (demand for dinosaurs) x1 0, x2 0 (non-negativity constraints) b) Solve the problem graphically (your answer should include the identification of the feasible region, optimal solution (objective function, decision variables), binding constraints and isoprofit line). H D 40 0 10 50 80 C E A 100 80 B G F 20 40 60 Feasible 20 30 x x Optimal Solution Z*=180 x1*=20 x2* = 60 Gradient Binding constraints Isoprofit lines
c) Convert the LP to the augmented form. Max z = 3 x1 + 2 x2 +0 x3 + 0x4 Subject to: 2 x1 + x2 + x3 = 100 x1 + x2 +x4 = 80 x1 x5 = 40 x1 0, x2 0 d) Show the correspondence between the Corner Points (A,B,C,D,E,F,G,H) and basic solutions. Characterize each basic solution in terms of: basic variables and corresponding values, non-basic variables and corresponding variable values, and

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info372-hwk6-sol - INFO 372 Homework 6 Due date Tuesday May...

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