1. **State the problem:** Find the number of book gambar ($x$) and book tulis ($y$) to maximize profit given resource constraints. 2. **Define variables:** Let $x$ = number of buku gambar produced Let $y$ = number of buku tulis produced 3. **Constraints:** - Kertas: $5x + 4y \leq 100$ - Perekat: $2x + y \leq 30$ - Non-negativity: $x \geq 0$, $y \geq 0$ 4. **Objective function (profit to maximize):** $$Z = 300x + 200y$$ 5. **Method: graphical linear programming with shifting objective line:** Plot constraints and find feasible region intersections. - Intersections: - When $y=0$ in kertas constraint: $5x = 100 \Rightarrow x=20$ - When $x=0$ in kertas constraint: $4y=100 \Rightarrow y=25$ - When $y=0$ in perekat constraint: $2x=30 \Rightarrow x=15$ - When $x=0$ in perekat constraint: $y=30$ - Intersection of constraints: Solve: $$5x+4y=100$$ $$2x+y=30$$ Multiply second by 4: $$8x + 4y =120$$ Subtract first: $$(8x+4y)-(5x+4y)=120-100 \Rightarrow 3x=20 \Rightarrow x=\frac{20}{3} \approx 6.67$$ Substitute into $2x+y=30$: $$2(6.67) + y =30 \Rightarrow 13.33 + y=30 \Rightarrow y=16.67$$ 6. **Feasible corner points:** - A$(0,0)$: $Z=0$ - B$(0,25)$: $Z=300(0)+200(25)=5000$ - C$(6.67,16.67)$: $Z=300(6.67)+200(16.67)=2001+3334=5335$ - D$(15,0)$: $Z=300(15)=4500$ 7. **Check which gives maximum profit:** Point C (approx. $(6.67,16.67)$) gives maximum profit $Z=5335$. 8. **Conclusion:** The company should produce approximately 7 buku gambar and 17 buku tulis to maximize profit with $Z \approx 5335$.