For the following problem, formulate the LP. DO NOT SOLVE. (Hint: Double Scripted Variables) 4. The Roadnet Transport Company expanded its shipping capacity by purchasing 75 trailer trucks from a bankrupt competitor. The company subsequently located 25 of the purchased trucks at each of its shipping warehouses in Charlotte, Memphis, and Louisville. The company makes shipments from each of these warehouses to terminals in St. Louis, Atlanta, and New York. Each truck is capable of making one shipment per week. The terminal managers have indicated their capacity for extra shipments. The manager at St. Louis can accommodate 42 additional trucks per week, the manager at Atlanta can accommodate 30 additional trucks, and the manager at New York can accommodate 26 additional trucks. The company makes the following profit per truckload shipment from each warehouse to each terminal. The profits differ as a result of differences in products shipped, shipping costs, and transport rates: Warehouse Charlotte Memphis Louisville St. Louis $1600 1220 1350 Atlanta $2050 740 860 New York $1650 900 2100 The company wants to know how many trucks to assign to each route (i.e., warehouse terminal) to maximize profit. (5 points) For each of the following problems, formulate the LP and solve using the simplex method: (The LP is given for problem 1 and 2.) 5. Solve the LP: (10 points) X1 - # of bowls, X2 = # of mugs Max Z-18 X1 + 24 X2 2 XI + 6 X2 =0 6. The Pinewood Furniture Company produces chairs and tables from two resources-labor and wood. The company has 12 hours of labor and 16 pounds of wood available each day. Demand for chairs is limited to 3 per day. Each chair requires 2 hours of labor and 3 pounds of wood to produce, while a table requires 4 hours of labor and 2 pounds of wood. The profit derived from each chair is $40 and from each table, $30. The company wants to determine the number of chairs and tables to produce each day to maximize profit. (10 points) Xi = # of chairs, X2 = # of tables Max Z=$40 X1 + $30 X2 2 X1 + 3 X2 =0 7. The Morris family owns 210 acres of farmland in North Carolina on which they grow corn and cotton. Each acre of corn costs $225 to plant, cultivate, and harvest; each acre of cotton costs $400. The Morris has a budget of $105,000 for next year. The government limits the number of acres of cotton they can plant to 100. The revenue from each acre of cotton is $625 and $375 for each acre of com. How many acres of each crop should they plant in order to maximize profit? Form L.P., in Standard and "Canonical" form and then solve using the simplex method. (10 points) For each of the following LPs, solve using the simplex method. 8. (10 points) Min Z-4X1 + 2X ST: 3X1 + X2 26 X1 + X2 24 X1X, 20 9. (10 points) Min Z = 4x + 5x2 ST: Xi+2X225 6X1 + 6X18 X.X20 For the following problem, formulate the LP. DO NOT SOLVE. (Hint: Double Scripted Variables) 4. The Roadnet Transport Company expanded its shipping capacity by purchasing 75 trailer trucks from a bankrupt competitor. The company subsequently located 25 of the purchased trucks at each of its shipping warehouses in Charlotte, Memphis, and Louisville. The company makes shipments from each of these warehouses to terminals in St. Louis, Atlanta, and New York. Each truck is capable of making one shipment per week. The terminal managers have indicated their capacity for extra shipments. The manager at St. Louis can accommodate 42 additional trucks per week, the manager at Atlanta can accommodate 30 additional trucks, and the manager at New York can accommodate 26 additional trucks. The company makes the following profit per truckload shipment from each warehouse to each terminal. The profits differ as a result of differences in products shipped, shipping costs, and transport rates: Warehouse Charlotte Memphis Louisville St. Louis $1600 1220 1350 Atlanta $2050 740 860 New York $1650 900 2100 The company wants to know how many trucks to assign to each route (i.e., warehouse terminal) to maximize profit. (5 points) For each of the following problems, formulate the LP and solve using the simplex method: (The LP is given for problem 1 and 2.) 5. Solve the LP: (10 points) X1 - # of bowls, X2 = # of mugs Max Z-18 X1 + 24 X2 2 XI + 6 X2 =0 6. The Pinewood Furniture Company produces chairs and tables from two resources-labor and wood. The company has 12 hours of labor and 16 pounds of wood available each day. Demand for chairs is limited to 3 per day. Each chair requires 2 hours of labor and 3 pounds of wood to produce, while a table requires 4 hours of labor and 2 pounds of wood. The profit derived from each chair is $40 and from each table, $30. The company wants to determine the number of chairs and tables to produce each day to maximize profit. (10 points) Xi = # of chairs, X2 = # of tables Max Z=$40 X1 + $30 X2 2 X1 + 3 X2 =0 7. The Morris family owns 210 acres of farmland in North Carolina on which they grow corn and cotton. Each acre of corn costs $225 to plant, cultivate, and harvest; each acre of cotton costs $400. The Morris has a budget of $105,000 for next year. The government limits the number of acres of cotton they can plant to 100. The revenue from each acre of cotton is $625 and $375 for each acre of com. How many acres of each crop should they plant in order to maximize profit? Form L.P., in Standard and "Canonical" form and then solve using the simplex method. (10 points) For each of the following LPs, solve using the simplex method. 8. (10 points) Min Z-4X1 + 2X ST: 3X1 + X2 26 X1 + X2 24 X1X, 20 9. (10 points) Min Z = 4x + 5x2 ST: Xi+2X225 6X1 + 6X18 X.X20