To find the highest price that cannot be paid with any combination of the two coins worth 7 cents and 11 cents, we can use a concept called the "Frobenius coin problem" or the "coin change problem."
Let's start by finding the greatest common divisor (GCD) of the two coin values, which is 1 in this case. Next, we can apply a formula to calculate the highest price that cannot be paid:
Highest Price = (Value of Coin 1 * Value of Coin 2) - (Value of Coin 1 + Value of Coin 2)
In this case, substituting the values, we have:
Highest Price = (7 * 11) - (7 + 11) = 77 - 18 = 59 cents
Therefore, the highest price that cannot be paid with any combination of the two coins is 59 cents.
It's important to note that this solution assumes that an unlimited number of coins is available for each denomination. Additionally, this problem assumes that only whole numbers of cents can be paid, so fractional values are not considered.