CUET · MATHS · PYQ PAPER 2023
Difference between the maximum and minimum value of the objective function \(Z=5 x+3 y\), subject to the constraints: \(3 x+5 y \leq 15 ; 5 x+2 y \leq 10 ; x, y \geq 0\) is:
- A \(\frac{45}{19}\)
- B \(\frac{235}{19}\)
- C \(\frac{64}{19}\)
- D 10
Answer & Solution
Correct Answer
(B) \(\frac{235}{19}\)
Step-by-step Solution
Detailed explanation
\(Z(0,0) = 5(0)+3(0) = 0\) \(Z(2,0) = 5(2)+3(0) = 10\) \(Z(0,3) = 5(0)+3(3) = 9\) \(Z(\frac{20}{19}, \frac{45}{19}) = 5(\frac{20}{19}) + 3(\frac{45}{19}) = \frac{100}{19} + \frac{135}{19} = \frac{235}{19}\) \(\text{Maximum value} = \frac{235}{19}\) \(\text{Minimum value} = 0\)…
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