Linear Programming Questions (5)

Determine the maximum value of \(z = 2x + 3y\), if the feasible region for an LPP is \(x + y \leq 4,\, x \geq 0,\, y \geq 0\).

Determine the minimum value of \(z = 3x + 5y\), if the feasible region for an LPP is \(x + 2y \geq 10,\, x + y \geq 6,\, 3x + y \geq 8,\, x \geq 0,\, y \geq 0\).

In the shaded region bounded by y = 3x and y = x/2, if P(a1, a2) lies in the shaded region, then for any point R(x, y) in the shaded region, \(y > \dfrac{x}{2}\) and \(y

Determine the minimum value of \(z = 3x + 2y\), if the feasible region for an LPP is shown in the following figure. (Corner points: \(D(0,10)\), \(C(1,5)\), \(B(4,2)\), \(A(12,0)\))

The feasible region for an LPP is shown in the following figure. Let \(z = 3x - 4y\) be the objective function. Maximum value of \(z\) is. (Corner points: \((0,4)\), \((6,0)\), \((12,6)\))