Question 1

Explanation

We will determine the coop dimensions and the number of panels needed.

Coop Dimension Analysis

Given:

• Coop height $= 3 \text{ m}$.
• Base area $= 256 \text{ m}^2$.
• Panel size $= 80 \text{ cm} \times 300 \text{ cm} = 0.8 \text{ m} \times 3 \text{ m}$.

Since the panel height matches the coop height ($3 \text{ m}$), panels are installed vertically. To avoid cutting, the length and width of the coop must be multiples of the panel width, which is $0.8 \text{ m}$.

Width constraint ($w$):

We look for multiples of $0.8$ within that range:

• $0.8 \times 7 = 5.6$
• $0.8 \times 8 = 6.4$
• $0.8 \times 9 = 7.2$

Check corresponding length ($l$) so that area is $256$ and $l$ is also a multiple of $0.8$:

1. If $w = 5.6$, then $l = \frac{256}{5.6} \approx 45.71$ (Not a multiple of $0.8$).
2. If $w = 6.4$, then $l = \frac{256}{6.4} = 40$. Check multiple: $\frac{40}{0.8} = 50$ (Valid).
3. If $w = 7.2$, then $l = \frac{256}{7.2} \approx 35.56$ (Not a multiple of $0.8$).

So, the possible coop dimensions are width $6.4 \text{ m}$ and length $40 \text{ m}$.

Calculating Number of Panels

Number of panels for width side:

Number of panels for length side:

Total panels needed to surround the coop (2 width sides + 2 length sides):

Calculating Cost

The price of one panel is $\text{Rp}40,000.00$.

Thus, the required cost is $\text{Rp}4,640,000.00$.