Complete on XCEL & show work
B) Carl Spackler is the Assistant Groundskeeper at a local country club. He wants to develop a new fertilizer at minimum cost. To do so, he will combine two ingredients, A and B, which cost $4 and $3 per pound, respectively. The final combination must contain at least 11 pounds of phosphate, at least 5 pounds of nitrate, and at least 2 pounds of a special compound found only in ingredient B. Ingredient A contains 10% phosphate and 25% nitrate. Ingredient B contains 20% phosphate, 5% nitrate, and 10% special compound. How many pounds of each ingredient are required to make the new fertilizer, and at what cost? B.16 The Arden County, Maryland, superintendent of education is responsible for assigning students to the three high schools in his county. He recognizes the need to bus a certain number of students, for several sectors of the county are beyond walking distance to 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. He also rec- ognizes that 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 him because he can walk to school. The three schools are located in sectors B, C, and E. The accompanying table reflects the number of high-school-age students living in each sector and the distance in miles from each sector to each school. DISTANCE TO SCHOOL SCHOOL IN SCHOOL IN SCHOOL IN SECTOR B SECTOR C SECTOR E NUMBER OF STUDENTS SECTOR 8 A B 5 0 4 7 12 4 0 6 12 7 5 0 700 500 100 800 400 2,500 D 2 7 E a) Each high school has a capacity of 900 students. Set up the objective function and constraints of this problem using linear programming so that the total number of student miles traveled by bus is minimized. Solve the problem. b) Boston's famous Limoges Restaurant is open 24 hours a day. Servers report for duty at 3 A.M., 7 A.M., 11 A.M., 3 P.M., 7 P.M., or 11 P.M., and each works an 8-hour shift. The following table shows the minimum number of workers needed during the 6 periods into which the day is divided. PERIOD TIME NUMBER OF SERVERS REQUIRED 1 2 3 4 5 6 3 A.M.-7 A.M. 7 A.M.-11 A.M. 11 A.M.-3 P.M. 3 P.M.7 P.M. 7 P.M.-11 P.M. 11 P.M.-3 A.M. 3 12 16 9 11 4 Owner Michelle Limoges scheduling problem is to determine how many servers should report for work at the start of each time period in order to minimize the total staff required for one day's operation. (Hint: Let X; equal the number of servers beginning work in time period i, where i = 1, 2, 3, 4, 5, 6.) B) Carl Spackler is the Assistant Groundskeeper at a local country club. He wants to develop a new fertilizer at minimum cost. To do so, he will combine two ingredients, A and B, which cost $4 and $3 per pound, respectively. The final combination must contain at least 11 pounds of phosphate, at least 5 pounds of nitrate, and at least 2 pounds of a special compound found only in ingredient B. Ingredient A contains 10% phosphate and 25% nitrate. Ingredient B contains 20% phosphate, 5% nitrate, and 10% special compound. How many pounds of each ingredient are required to make the new fertilizer, and at what cost? B.16 The Arden County, Maryland, superintendent of education is responsible for assigning students to the three high schools in his county. He recognizes the need to bus a certain number of students, for several sectors of the county are beyond walking distance to 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. He also rec- ognizes that 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 him because he can walk to school. The three schools are located in sectors B, C, and E. The accompanying table reflects the number of high-school-age students living in each sector and the distance in miles from each sector to each school. DISTANCE TO SCHOOL SCHOOL IN SCHOOL IN SCHOOL IN SECTOR B SECTOR C SECTOR E NUMBER OF STUDENTS SECTOR 8 A B 5 0 4 7 12 4 0 6 12 7 5 0 700 500 100 800 400 2,500 D 2 7 E a) Each high school has a capacity of 900 students. Set up the objective function and constraints of this problem using linear programming so that the total number of student miles traveled by bus is minimized. Solve the problem. b) Boston's famous Limoges Restaurant is open 24 hours a day. Servers report for duty at 3 A.M., 7 A.M., 11 A.M., 3 P.M., 7 P.M., or 11 P.M., and each works an 8-hour shift. The following table shows the minimum number of workers needed during the 6 periods into which the day is divided. PERIOD TIME NUMBER OF SERVERS REQUIRED 1 2 3 4 5 6 3 A.M.-7 A.M. 7 A.M.-11 A.M. 11 A.M.-3 P.M. 3 P.M.7 P.M. 7 P.M.-11 P.M. 11 P.M.-3 A.M. 3 12 16 9 11 4 Owner Michelle Limoges scheduling problem is to determine how many servers should report for work at the start of each time period in order to minimize the total staff required for one day's operation. (Hint: Let X; equal the number of servers beginning work in time period i, where i = 1, 2, 3, 4, 5, 6.)
