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A cargo helicopter delivers only 100-pound packages and 120-pound packages. For each delivery trip, the helicopter must carry at least 10 packages, and the total weight of the packages can be at most 1,100 pounds. What is the maximum number of 120-pound packages that the helicopter can carry per trip?

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sqdancefan

Answer:

  5

Step-by-step explanation:

A graphical solution shows the number of 120-pound packages can be at most 5.

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In the graphical solution, the doubly-shaded area is the "feasible region". Its maximum extent in the "120-pound packages" direction is 5.

Ver imagen sqdancefan

Maximum number of 120 pound packages helicopter can carry is 5.

Step-by-step explanation:

Let m be the number of 100 pond packages and n be the number of 120 pound packages.

For each delivery trip, the helicopter must carry at least 10 packages.

          m + n ≥ 10

          m ≥ 10 - n

Total weight of the packages can be at most 1,100 pounds

         100m + 120 n ≤ 1100  

         10 m + 12 n  ≤ 110

         5 m + 6 n  ≤ 55  

          5 (10 - n ) + 6 n  ≤ 55

          50 - 5n + 6 n ≤ 55

                      n ≤ 5

So maximum number of 120 pound packages helicopter can carry is 5.

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