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The corner points of the feasible region determined by the system of linear constraints are (0,0), (0, 40), (20, 40), (60, 20) and (60, 0). If the objective function of an LPP is $Z=4x+3y$, then the maximum value is :
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Q: The corner points of the feasible region determined by the system of linear constraints are (0,0), (0, 40), (20, 40), (60, 20) and (60, 0). If the objective function of an LPP is $Z=4x+3y$, then the maximum value is :

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Detailed Solution

Step 1: Identify the Objective Function

The objective function is given by Z = 4x + 3y. We need to evaluate this function at each of the provided corner points of the feasible region.

Step 2: Evaluate Z at each corner point

We substitute the coordinates (x, y) into the objective function:

  • At (0, 0): Z = 4(0) + 3(0) = 0
  • At (0, 40): Z = 4(0) + 3(40) = 120
  • At (20, 40): Z = 4(20) + 3(40) = 80 + 120 = 200
  • At (60, 20): Z = 4(60) + 3(20) = 240 + 60 = 300
  • At (60, 0): Z = 4(60) + 3(0) = 240

Step 3: Determine the Maximum Value

Comparing the calculated values {0, 120, 200, 300, 240}, the maximum value is 300, which occurs at the point (60, 20).

Final Answer: 300

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