Problem 6-09 (Algorithmic) The Ace Manufacturing Company has orders for three similar products: Product Order (Units) 2150 B 550 C 1200 Three machines are available for the manufacturing operations. All three machines can produce all the products at the same production rate. However, due to varying defect percentages of each product on each machine, the unit costs of the products vary depending on the machine used. Machine capacities for the next week and the unit costs are as follows: Machine Capacity (Units) 1450 1600 W N 900 Product Machine A B $0.80 $1.20 $0.70 2 $1.20 $1.30 $1.20 $0.90 $0.90 $1.20 Use the transportation model to develop the minimum cost production schedule for the products and machines. Show the linear programming formulation. If the constant is "1" it must be entered in the box. If your answer is zero enter "0". The linear programming formulation and optimal solution are shown. Let xij = Units of product j on machine i. Min X14 X1B X1C * 2A X 28 X 2C X3A X 38 X3C s.t. X1A X18 xIC X2A X2B x2C + X3A X3B + x3c X14 + X2A X3A X1B X2B X3B x1c X2C X3C xij 2 0 for all i, j If required, round your answers to the nearest whole number. Optimal Solution Units Cost 1-A $ 1-B $ 1 - C $ 2-A $ 2 - B $ 2-C $ 3-A $ 3 -E $ 3-C Total $Problem 6-19 (Algorithmic) A local television station plans to drop four Friday evening programs at the end of the season. Steve Botuchis, the station manager, developed a list of six potential replacement programs. Estimates of the advertising revenue ($) that can be expected for each of the new programs in the four vacated time slots are as follows. Mr. Botuchis asked you to find the assignment of programs to time slots that will maximize total advertising revenue. 5:00 - 5:30 P.M. 5:30 - 6:00 P.M. 7:00 - 7:30 P.M. 8:00 - 8:30 P.M. Comedy Live 5500 3500 5500 4500 World News 7500 7000 8000 5500 NASCAR Live 7500 5500 5500 7500 Wall Street Today 8500 6500 6500 5000 Hollywood Briefings 8500 7500 3000 6000 This Week in Hockey 6500 4000 4500 8000 Choose the assignment of programs to time slots that will maximize total advertising revenue. Time slot Program 5:00-5:30 p.m. Wall Street Today 5:30-6:00 p.m. Hollywood Briefings 7:00-7:30 p.m. World News 8:00-8:30 p.m. This Week in Hockey V Total expected advertising revenue = $Problem 6-23 (Algorithmic) Find the shortest route from node 1 to node 7 in the network shown. If the constant is "1" it must be entered in the box. If your answer is zero enter "0". For negative values enter "minus" sign (-). 10 14 17 20 12 Let bij : 1 if the arc from node i to node j is on the shortest route otherwise Min x12 + X13 - *14 + *23 + *25 x32 x35 - x46 + x52 + X53 X56 + *57 X65 + X67 s.t. Flow Out Flow In Node 1 x12 + x13 + X14 Node 2 x23 + X25 x12 + *32 + X52 Node 3 X32 + X35 x13 + x23 + X53 Node 4 X46 X14 X52 + *53 + x56 + Node 5 *25 x35 + X65 X57 Node 6 *65 + X67 X46+ X56 Node 7 x57 + X67 *ij 2 0 for all i and ] Optimal Solution: Variable Value X12 X13 X14 X23 X25 X32 X35 X46 X52 X53 X56 X57 X65 X57 Shortest Route: 1-2-5-7 - v Length =