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      Question

      A manufacturer produces two items A and B. Each unit of

      A requires 1 hour of labor and 2 units of raw material. Each unit of B requires 2 hours of labor and 1 unit of raw material. Labor is available for 100 hours and raw material for 80 units. What is the constraint on raw material?
      A x + 2y ≤ 80 Correct Answer Incorrect Answer
      B 2x + y ≤ 80 Correct Answer Incorrect Answer
      C x + y ≤ 80 Correct Answer Incorrect Answer
      D x + y ≥ 80 Correct Answer Incorrect Answer

      Solution

      Let x be the number of units of item A produced, and y be the number of units of item B produced. We are given the following information:

      • Each unit of A requires 2 units of raw material.
      • Each unit of B requires 1 unit of raw material.
      • The total raw material available is 80 units.
      The total amount of raw material used to produce x units of A and y units of B can be expressed as: Raw material used = (Raw material per unit of A) × (Number of units of A) + (Raw material per unit of B) × (Number of units of B) Raw material used = 2×x+1×y=2x+y The total raw material used cannot exceed the total raw material available. Therefore, the constraint on raw material is: 2x+y≤8

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