Please write the objective function and R codes I do not need the parts f-g

2. A chemical manufacturer is interested in finding the optimal allocation of reaction columns for six petroleum products, P1, P2, P3, P4, P5 and P6. He has columns A, B, C, and D at his disposal. We know that A can produce any of the chemicals, B and C can produce P1, P2, P3 and Pe, and column D is specialized to produce Pa, Ps and Pe. 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 P P2 P3 PA PS D Demand 523 721 639 0 21,000 419 615 492 0 5,000 563 709 515 0 2,000 315 0 0 330 1,200 292 0 0407 1,400 312 314 309 291 4,300 Po (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