Sensitivity in Linear Programming

4. A cargo barge has two compartments for storing cargo: forward and rear. These com- partments have the limitations on volume and weight shown in Table 5.5. To enable the barge to safely pass through some shallow areas, 40% of the weight must be in the forward compartment and 60% in the rear. The barge owner has 3 cargoes available for the next trip, and the data on these cargoes are shown in the lower section of Table 5.5. Any portion of each cargo may be shipped. The shipper needs to know how much of each cargo to ship and how to load the cargo in the two compartments in order to maximize profit for this barge for the trip. How would the problem change if the balancing condition were replaced by the requirement that not less than 40% and not more than 45% of the weight be in the forward compartment? Table 5.5 Barge Data Compartment Capacity Weight (tons) Space (cu ft) 8 5000 12 7000 Forward Rear Cargo Data Cargo Weight (tons) Volume (cu ft/ton) Profit ($/ton) 1 2 3 14 22 9 500 700 400 100 130 90 Solve the version of the problem where between 40% and 45% of the weight must be forward