1. **State the problem:** We are asked how many lines will be in the graph of the linear program with constraints: $$9P + 5Q \geq 45$$ $$Q \leq 6$$ $$P \leq 3$$ $$P \geq 0, Q \geq 0$$ 2. **Identify each constraint as a line:** - The inequality $9P + 5Q \geq 45$ corresponds to the line $9P + 5Q = 45$. - The inequality $Q \leq 6$ corresponds to the line $Q = 6$. - The inequality $P \leq 3$ corresponds to the line $P = 3$. - The inequalities $P \geq 0$ and $Q \geq 0$ correspond to the coordinate axes lines $P=0$ and $Q=0$. 3. **Count the lines:** - $9P + 5Q = 45$ - $Q = 6$ - $P = 3$ - $P = 0$ - $Q = 0$ There are 5 lines in total. **Final answer:** 5