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What is the maximum value of z, if z = 10x + 6y subject to the constrains 3x + y ≤ 12, 2x + 5y ≤ 34, x ≥ 0, y ≥ 0 ?

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  1. 56
  2. 52
  3. 50
  4. 40

Answer (Detailed Solution Below)

Option 1 : 56
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Detailed Solution

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The given two equations are: 3x + y ≤ 12 and 2x + 5y ≤ 34

For the given equations, the graph is as shown below.

From the above graph, the extreme points are: (4, 0), (0, 6.8) and (2, 6)

z = 10x + 6y

At (4, 0), z = 10(4) + 6(0) = 40

At (0, 6.8), f(X, Y) = 10(0) + 6(6.8) = 40.8

At (2, 6) = 10(2) + 6(6) = 56

The maximum value of z = 56

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