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The corner point of the feasible solutio...

The corner point of the feasible solutions are(0,0) (3,0)(2,1)(0,7/3) the maximum value of Z= 4x+5y is

A

12

B

13

C

35/3

D

0

Text Solution

AI Generated Solution

The correct Answer is:
To find the maximum value of \( Z = 4x + 5y \) at the corner points of the feasible solutions, we will evaluate the function at each of the given corner points: \( (0,0) \), \( (3,0) \), \( (2,1) \), and \( (0,\frac{7}{3}) \). ### Step-by-Step Solution: 1. **Evaluate \( Z \) at \( (0,0) \)**: \[ Z = 4(0) + 5(0) = 0 \] 2. **Evaluate \( Z \) at \( (3,0) \)**: \[ Z = 4(3) + 5(0) = 12 \] 3. **Evaluate \( Z \) at \( (2,1) \)**: \[ Z = 4(2) + 5(1) = 8 + 5 = 13 \] 4. **Evaluate \( Z \) at \( (0,\frac{7}{3}) \)**: \[ Z = 4(0) + 5\left(\frac{7}{3}\right) = \frac{35}{3} \approx 11.67 \] 5. **Compare the values of \( Z \)**: - At \( (0,0) \), \( Z = 0 \) - At \( (3,0) \), \( Z = 12 \) - At \( (2,1) \), \( Z = 13 \) - At \( (0,\frac{7}{3}) \), \( Z \approx 11.67 \) 6. **Determine the maximum value**: The maximum value of \( Z \) occurs at the point \( (2,1) \) where \( Z = 13 \). ### Final Answer: The maximum value of \( Z = 4x + 5y \) is **13**. ---
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State True or False: If the corner points of the feasible region are (0, 7/3),(2,1),(3, 0) & (0,0) then the maximum value of Z = 4x + 5y is 12 .

State True or False: If the corner points of the feasible region are (0, 10),(2, 2) & (4, 0) then the minimum value of Z = 3x + 2y is at (4, 0)

Knowledge Check

  • If a corner points of the feasible solutions are (0,10)(2,2)(4,0) (3,2) then the point of minimum Z=3x +2y is

    A
    (2,2)
    B
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    20
    B
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    D
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  • The corner points of the feasible region are (4, 2), (5,0), (4,1) and (6,0) then the point of minimum z = 3.5x + 2y= 16 is at

    A
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    B
    (5,0)
    C
    (6,0)
    D
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