For options with the same style (European or American) and expiry date, you are given:

(i) 40-strike put options on a stock have price 1

(ii) 70-strike put options on a stock have price 10

Determine, based on convexity of option prices, the highest possible price for a 60-strike put option, and determine the number of 40- and 70- strike put options needed to guarantee a payoff at expiry at least as large as the payoff of one 60-strike put option.