As a seismologist, Hector understands the devastating effects that earthquakes can have. So, he keeps his basement stocked with canned food, like chili. Hector buys cans of chili from an online retailer that charges a shipping fee plus the cost of each can of chili.

To determine if x (the number of cans) and y (the total cost) have a proportional relationship, we need to see if the ratio \( \frac{y}{x} \) is the same for all the given pairs of values.

Let's compute the ratios for each pair:

1. For \( x = 40 \) and \( y = 50 \): \[ \frac{y}{x} = \frac{50}{40} = 1.25 \]

2. For \( x = 46 \) and \( y = 56 \): \[ \frac{y}{x} = \frac{56}{46} = \frac{28}{23} \approx 1.217 \]

3. For \( x = 77 \) and \( y = 87 \): \[ \frac{y}{x} = \frac{87}{77} \approx 1.129 \]

4. For \( x = 99 \) and \( y = 109 \): \[ \frac{y}{x} = \frac{109}{99} \approx 1.101 \]

As we can see, the ratios are not consistent across all pairs of values. Since the ratio \( \frac{y}{x} \) is different for each value of x, we conclude that \( x \) and \( y \) do not have a proportional relationship.

Therefore, the answer is no.