MAN 256 INTRODUCTION TO MANAGEMENT SCIENCE Spring 2007 Exam I Dr. Y. Günalay Closed book and notes. NAME: __ SOLUTION SET __ Show all your work... Please try to use the space that was provided for each question. Do not write more than required. Use of mobile devices are strongly forbidden! Duration: 75 minutes Question 1. (30 points) John Hoke owns Hoke’s Spokes, a bicycle shop. Most of John’s bicycle sales are customer orders; however, he also stocks bicycles for walk-in customers. He stocks 3 types of bicycles: road-racing, cross-country, and mountain. A road-racing bike costs $1,200, a cross-country bike costs $1,700, and a mountain bike costs $900. He sells road-racing bikes for $1,800, cross-country bikes for $2,100, and mountain bikes for $1,200. He has $12,000 available this month to purchase bikes. Each bike must be assembled; a road-racing bike requires 8 hours to assemble, a cross-country bike requires 12 hours, and a mountain bike requires 16 hours. He estimates that he and his workers have 120 hours available to assemble bikes. He has enough space in his store to order 20 bikes this month. Based on past sales, John wants to stock at least twice as many mountain bikes as the other two combined because mountain bikes sell better. I have formulated a LP model for John: Let r, c, and m denote number of road-racing, cross-country, and mountain bikes to order this month, respectively. Max Z = 600r + 400c +300m st 1200r + 1700c + 900m ≤ 12000 (budget constraint) 8r + 12c +16m ≤ 120 (assembly time constraint) r + c + m ≤ 20 (space constraint) -2r – 2c + m ≥ 0 (marketing constraint) r, c, m ≥ 0 I have also solved the above model using Solver. The Solver output showing the optimal solution and the sensitivity analysis report are on the next page.

Bicycles Road-racing Cross-country Mountain Profit Unit profit 600 400 300 3600 Opt values 3 0 6 Constraints LHS RHS Budget 1200 1700 900 9000 < 12000 Assembly 8 12 16 120 < 120 Space 1 1 1 9 < 20 Marketing -2 -2 1 0 > 0 Adjustable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$3 Opt values Road-racing 3 0 600 1E+30 290.909 $C$3 Opt values Cross-country 0 -320 400 320 1E+30 $D$3 Opt values Mountain 6 0 300 900 600 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $E$5 Budget LHS 9000 0 12000 1E+30 3000 $E$6 Assembly LHS 120 30 120 40 120 $E$7 Space LHS 9 0 20 1E+30 11 $E$8 Marketing LHS 0 -180 0 7.5 10