Covaxin vs Covishield

There are two types of vaccines available: Covaxin and Covishield. A black marketeer has $X$ coins and wants to buy as many vaccines as possible. Due to the black marketing concerns, government has enforced the following policy: - $i^{th}$ dose of Covaxin costs $a + (i - 1)\cdot b$ coins for every $i \geq 1$. - $i^{th}$ dose of Covishield costs $c + (i - 1)\cdot d$ coins for every $i \geq 1$.