3-34 Determine value of objective function and decision variables. Problem 5-12 Determine value of objective function and decision variables. 3-34 A steel company is producing steel for a new contract. The contract specifies the information in the following table for the steel. MATERIAL MINIMUM MAXIMUM Maganese 2.10% 3.10% Silicon 4.30% 6.30% Carbon 1.05% 2.05% The steel company mixes batches of eight different available materials to produce each ton of steel according to the specification. The table at the bottom of this page details these materials. Formulate and solve the LP model that will indicate how much of each of the eight materials should be blended into a 1-ton load of steel so that the company can meet the specifications under the contract while minimizing costs. MATERIAL MANGANE SILICON CARBON POUNDS COST PER AVAILABLE SE AVAILABLE POUND Alloy 1 70.0% 15.0% 3.0% No Limit $0.12 Alloy 2 55.0% 30.0% 1.0% 300 $0.13 Alloy 3 12.0% 26.0% 0% No Limit $0.15 Iron 1 1.0% 10.0% 3.0% No Limit $0.09 Iron 2 5.0% 2.5% 0% No Limit $0.07 Carbide 1 0% 24.% 18.0% 50 $0.10 Carbide 2 0% 25.0% 20.0% 200 $0.12 Carbide 3 0% 23.% 25.0% 100 $0.09 5-12 The Oconee County, South Carolina, superintendent of education is responsible for assigning students to the three high schools in his county. A certain number of students have to travel to and from school by bus, as several sectors of the county are beyond walking distance from a school. The superintendent partitions the county into five geographic sectors as he attempts to establish a plan that will minimize the total number of student miles traveled by bus. Of course, if a student happens to live in a certain sector and is assigned to the high school in that sector, there is no need to bus that student because he or she can walk to school. The three schools are located in sectors B, C, and E. The table below reflects the number of high school age students living in each sector and the distance, in miles, from each sector to each school. Assuming that each high school has a capacity of 1,100 students, set up and solve Oconee County's problem as a transportation model. DISTANCE TO SCHOOLS IN MILES SECTOR SECTOR SECTOR SECTOR NUMBER OF B C E STUDENTS A 6 7 11 800 B 0 3 10 600 C 9 0 6 400 D 8 3 5 700 E 15 8 0 500