Solve the following linear programming problem graphically: Maximise `Z = 4x +y` . . . (1) , subject to the constraints:`x+ylt=50` . . .(2), `3x+ylt=90` . . .(3) , `xgeq0,ygeq0` . . .(4)

Explanation

To solve the linear programming problem graphically, we need to maximize the objective function \( Z = 4x + y \) subject to the given constraints. Here are the steps to find the solution:

### Step 1: Identify the Constraints
The constraints given are:
1. \( x + y \leq 50 \) (Constraint 1)
2. \( 3x + y \leq 90 \) (Constraint 2)
3. \( x \geq 0 \) (Constraint 3)
4. \( y \geq 0 \) (Constraint 4)
...