A speculator is considering the purchase of a commodity which he reckons has a $40\%$ chance of increasing in value over the next month. If he purchases the commodity and it does increase in value the speculator will make a profit of about $$100,000,$ otherwise he will lose $$40,000.$a$)$ Assuming that the expected monetary value criterion is applicable, determine whether the speculator should purchase the commodity.b$)$ Perform a sensitivity analysis on the speculator's estimate of the probability of a price increase and interpret your result.What reservations would you have about applying the expected monetary value criterion in this context?