Lpp Graphical Method

Concept: In linear programming, optimal value occurs at extreme points.

Step 1: Feasible region.
It is a convex polygon.

Step 2: Key property.
Maximum/minimum occurs at vertices.

Step 1: Use inverse trigonometric identities.
We start with the equation: Let , then: Using the identity , we know that: Thus, and , where is a constant. Since , we get: Therefore, and .
Step 2: Solve for .
Now, using the given equation, we have: So, . Using the double angle identity for cosine: Substitute : Thus:
Final Answer: 4.