1. A chemical manufacturer is interested in finding the optimal allocation of reaction columns for six...

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1. A chemical manufacturer is interested in finding the optimal allocation of reaction columns for six petroleum products, P₁, P2, P3, P4, Ps, P6 and P. He has reaction columns A, B, and Cat his disposal. We know that A can produce any of the chemicals, B and C can produce P1, P2, P3, P and P7. He needs to determine what to produce on which machines given the following information: The machines can produce each product at the following rates of litres per hour and Demand for the next 24 hours. Product A B C❘ Demand P₁ 523 721 639 21,000 P₂ 622 615 492 6,300 P3 624 709 512 6,400 PA 307 0 0 600 Ps 293 0 0 550 Po 309 314 304 1,800 P7 112 217 97 800 The cost of running each item on each machine per hour is: Product A B C P₁ 53 71 39 59 63 42 64 78 52 30 0 0 Ps 41 0 0 Po 72 83 26 P7 21 26 22 (a) (5pts) Clearly define the variables that will be optimized over (there may be alot of these). (b) (5pts) Clearly define the constraints using the variable notation above. (c) (10 pts) Define c, A and b for the linear program. (d) (10 pts) Write the R code that will solve the above linear program. (e) (5 pts) Write the solution from the linear program if it exists. (f) (10 pts) Write the solution to the linear program in a manner that a manner that a manager could employ... how about a schedule of what to run when and on what machine. (g) (5 pts) Conduct a sensitivity study to see how the solution changes if the constraints are mildly changed. 1. A chemical manufacturer is interested in finding the optimal allocation of reaction columns for six petroleum products, P₁, P2, P3, P4, Ps, P6 and P. He has reaction columns A, B, and Cat his disposal. We know that A can produce any of the chemicals, B and C can produce P1, P2, P3, P and P7. He needs to determine what to produce on which machines given the following information: The machines can produce each product at the following rates of litres per hour and Demand for the next 24 hours. Product A B C❘ Demand P₁ 523 721 639 21,000 P₂ 622 615 492 6,300 P3 624 709 512 6,400 PA 307 0 0 600 Ps 293 0 0 550 Po 309 314 304 1,800 P7 112 217 97 800 The cost of running each item on each machine per hour is: Product A B C P₁ 53 71 39 59 63 42 64 78 52 30 0 0 Ps 41 0 0 Po 72 83 26 P7 21 26 22 (a) (5pts) Clearly define the variables that will be optimized over (there may be alot of these). (b) (5pts) Clearly define the constraints using the variable notation above. (c) (10 pts) Define c, A and b for the linear program. (d) (10 pts) Write the R code that will solve the above linear program. (e) (5 pts) Write the solution from the linear program if it exists. (f) (10 pts) Write the solution to the linear program in a manner that a manner that a manager could employ... how about a schedule of what to run when and on what machine. (g) (5 pts) Conduct a sensitivity study to see how the solution changes if the constraints are mildly changed.

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well solve the linear programming step by step a Variables to be Optimized Let xij denote the quanti... View the full answer