KCET · Maths · Functions

The shaded region shown in fig. is given by the inequation

A \( 14 x+5 y \geq 70 ; y \leq 14 \) and \( x-y \leq 5 \)
B \( 14 x+5 y \geq 70 ; y \leq 14 \) and \( x-y \geq 5 \)
C \( 14 x+5 y \leq 70 ; y \leq 14 \) and \( x-y \geq 5 \)
D \( 14 x+5 y \geq 70 ; y \geq 14 \) and \( x-y \geq 5 \)

Verified Solution

Answer & Solution

Correct Answer

(A) \( 14 x+5 y \geq 70 ; y \leq 14 \) and \( x-y \leq 5 \)

Step-by-step Solution

Detailed explanation

Let points, \(A(0,14), B(5,0)\) and \(C(19,14)\)

Now, equation of side \(\mathrm{AB}\) is \(\frac{x}{5}+\frac{y}{14}=1\) \(\Rightarrow 14 x+5 y=70 \rightarrow(1)\) Equation of side \(\mathrm{AC}\) is \(y=14 \rightarrow(2)\) and equation of side \(\mathrm{BC}\) is \(x-y=5 \rightarrow(3)\) Therefore, the shaded region shown in figure is given by the inequation \(14 x+5 y>70 y < 14\) and \(x-y < 5\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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