Solve the linear programming problem. \( \begin{array}{l}\text { Maximize } \\ P=30 x+40 y \\ \text { Subject to } \\ \begin{aligned} 2 x+y & \leq 14 \\ x+y & \leq 8 \\ x+2 y & \leq 12 \\ x, y & \geq 0\end{aligned}\end{array} \).

18. \( \begin{aligned} y & =x-5 \\ y & =-2 x-5\end{aligned} \)

3.1.2 The number pattern is quadratic and \( T_{4}=2+5 y \). 3.2 In a linear number pattern, the \( 19^{\text {th }} \) term is 40 and the \( 7^{\text {th }} \) term is 16 . Thus, determine the first two terms.

D) A student claimed that the largest integer of \( k \) for which the graph \( y=2 x^{2}-3 x+k-1 \) meets the \( x \)-axis is 2 . Verify this statement.

Find the slope and the \( y \)-intercept of the graph of the equation. \[ 8 x+9 y=36 \] slope \( y \)-intercept \( \quad(x, y)=(\square) \)

प्रश्नाबानी 2.2 निम्न द्विघात बहुपदों के शून्यक ज्ञात कीजिए और शून्यकों तथा गुणांकों के बीच के संबंध की सत्यता की जाँच कीजिए : \( \begin{array}{lll}\text { (iv) } x^{2}-2 x-8 & \text { (ii) } 4 s^{2}-4 s+1 & \text { (iii) } 6 x^{2}-3-7 x \\ \text { (iv) } 4 u^{2}+8 u & \text { (v) } s^{2}-15 & \text { (vi) } 3 x^{2}-x-4\end{array} \)