Answer Happy

The Plant Manager of a plastic pipe manufacturing has the opportunity to use two different routings for a particular type of plastic pipe. Routing 1 uses extruder A and routing 2 uses extruder B. The following table shows the time requirements and capacities of these processes. Process Melting Extruder A Time Requirement (hr/100ft) Routing 1 1 3 0 Routing 2 |1 10 Capacity (hr) 45 90 Extruder B 1 30 Each 100 feet of pipe processed on Routing 1 uses 5 pounds of raw material, whereas each 100 feet of pipe processed on Routing 2 uses only 4 pounds. The difference results from differing scrap rates of the extruding machines. Consequently, the profit per 100 ft of pipe processed on Routing 1 is $60 and on Routing 2 is $80. A total of 200 pounds of raw material is available. i) Formulate a linear programming model for this problem. ii) Use the graphical solution method to find the optimal solution to this problem. iii) Use the coefficient sensitivity to determine the value of C₁, the profit unit processed on Routing 1, that would bring x, into the solution (make x, greater than 0) if Extruder B capacity is 160 hrs. (Ans: Z=$3300, C₁=80)