For three 6-month American call options on a stock, you are given the following information:

(i) One with strike price 45 sells for 6.30.

(ii) One with strike price 44 sells for 7.00.

(iii) One with strike price 40 sells for 9.50.

The option with strike 44 is overpriced based on the convexity property of option premiums. You therefore sell it and purchase x 40-strike calls and y 45-strike calls (note that we do not necessarily need to have x + y = 1). Determine the maximal and the minimal values of x and y in order to create an arbitrage