Question

Solve the following linear programming problem graphically:

Maximize Z=3X+5Y
Subject to:
4X+4Y≤48 C₁
1X+2Y≤20 C₂
y≥2 C₃
X, Y≥0
Using the line drawing tool, plot constraint C₁ by picking two endpoints for the line.

Answer 1

To solve the linear programming problem graphically, we need to plot the given constraints on a graph and find the feasible region. The objective is to maximize the function Z=3X+5Y. Let's start by plotting the constraint C₁: 4X+4Y≤48.

Step-by-step explanation:

To solve the linear programming problem graphically, we need to plot the given constraints on a graph and find the feasible region. The objective is to maximize the function Z=3X+5Y. Let's start by plotting the constraint C₁: 4X+4Y≤48. We can choose two endpoints for the line by assigning arbitrary values to X or Y and solving for the other variable. For example, if we let X=0, then 4Y≤48, which gives us Y≤12. If we let Y=0, then 4X≤48, which gives us X≤12. Plotting these two points on the graph and connecting them will give us the line for constraint C₁.