CONSIDER THE FOLLOWING LINEAR PROGRAM: Minimize C = 75P + 32Q Subject To: 9P + 5Q >= 45 (1) Q <= 6 (2) P <=3 (3) P>=0, Q>=0 If you place P in the horizontal axis, at what point will the line 9P + 5Q = 45 meet the vertical axis? 

To find where the line \( 9P + 5Q = 45 \) meets the vertical axis, we need to find the point where \( P = 0 \). 

When \( P = 0 \), the equation becomes:

\[
9(0) + 5Q = 45
\]

Simplifying:

\[
5Q = 45
\]

\[
Q = \frac{45}{5} = 9
\]

So, the line \( 9P + 5Q = 45 \) meets the vertical axis at the point \( (0, 9) \).

Would you like more details or have any questions?

Here are five related questions:
1. What is the intersection point of the line \( 9P + 5Q = 45 \) with the horizontal axis?
2. How do you graph the constraints on a \( P-Q \) plane?
3. What is the feasible region for this linear program based on the constraints?
4. How do we find the optimal solution to minimize \( C = 75P + 32Q \)?
5. How would the solution change if the objective function was maximized instead?

**Tip:** When solving linear programming problems graphically, always plot the constraint lines first to define the feasible region.

CONSIDER THE FOLLOWING LINEAR PROGRAM: Minimize C = 75P + 32Q Subject To: 9P + 5Q >= 45 (1) Q <= 6 (2) P <=3 (3) P>=0, Q>=0 If you place P in the horizontal axis, at what point will the line 9P + 5Q = 45 meet the vertical axis?

Learn how to solve a linear programming problem by graphing the constraint 9P + 5Q = 45. This problem focuses on finding the intersection with the vertical axis and is essential for students learning about graphing linear equations and constraints. Suitable for Grades 10-12.

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