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Worksheet: Finding the Maximum and Minimum Values of the Objective Function

Q1:

Using linear programming, find the minimum and maximum values of the function 𝑝 = 4 π‘₯ βˆ’ 3 𝑦 given that π‘₯ β‰₯ 0 , 𝑦 β‰₯ 0 , π‘₯ + 𝑦 ≀ 9 , and 𝑦 β‰₯ 5 .

  • AThe minimum value is βˆ’ 1 5 , and the maximum value is 1.
  • BThe minimum value is βˆ’ 2 7 , and the maximum value is βˆ’ 1 5 .
  • CThe minimum value is 0, and the maximum value is 9.
  • DThe minimum value is βˆ’ 2 7 , and the maximum value is 1.

Q2:

Determine the values of π‘₯ and 𝑦 that maximize the function 𝑝 = 5 π‘₯ + 2 𝑦 . Write your answer as a point ( π‘₯ , 𝑦 ) .

  • A ( 3 , 0 )
  • B ( 0 , 8 )
  • C ( 7 , 0 )
  • D ( 7 , 8 )