**Answer:**

a) The daily fee is $102

The processing fee is $42

b) The maximum number of days the beach house can be rented with no more than $1,200 is (by rounding down) 11 days

**Step-by-step explanation:**

The data given in the table are as follows;

Number of days (t) Total cost, T (dollars)

2 246

4 450

6 654

8 858

Whereby, we have that the processing fee is P, and the daily fee is D, we can write;

Total cost, T = D × t + P

From the table, we have;

When t = 2 days and T = $246, the above equation for total cost becomes;

$246 = D × 2 + P = 2·D + P

246 = 2·D + P.....(1)

Similarly, when t = 6 days, and T = $654, we have;

$654 = D × 6 + P = 6·D + P

654 = 6·D + P.....(2)

Subtracting equation (1) from equation (2) gives;

654 - 246 = 6·D + P - (2·D + P)

408 = 4·D

D = 408/4 = 102

The daily fee, D = $102

From equation (1), we have;

246 = 2·D + P = 2 × 102 + p

p = 246 - 2 × 102 = 42

P = $42

The processing fee, P = $42

b) Given that the maximum amount available (total amount) for spending on the beach house rental = $1200, we have;

T = D × t + P

Where, D = $102 and P = $42 are constants and T = $1,200, we have;

1,200 = 102 × t + 42

t = (1200 - 42)/102 ≈ 11.35 days

Given that we can only rent the beach house for a whole number of days, the number of days the beach house can be rented is therefore, by rounding down, t = 11 days.