This is known as a Frobenius problem, which is solved using the formula xy − x – y, where x and y represent the respective frobenius numbers.
If the company sells calculators only in packages of 11 and packages of 15, then x=11 and y=15.
The largest number of calculators it is not possible to purchase without opening a package is thus calculated as follows:
(11x15) – 11 – 15
= 165 – 11 – 15
=165 – 26
=139
If the company sells calculators only in packages of 11 and packages of 15, the largest number of calculators it is not possible to purchase without opening a package is 139