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(d) (9 pts) Suppose a different company offers Ludo Corporation a Loss Control service which costs S (in dollars) and which cuts the probability of all losses in half (such that the probability of both the small loss and the large loss are reduced to 1/6 rather than 1/3), meaning that the new probability distribution for the Ludo Corporation's pre-tax income is given by 100 S with prob. 2/3 70 - S with prob. 1/6 20 S with prob. 1/6 For what values of S will Ludo Corporation prefer to buy the Loss Control service instead of doing what you concluded it would do in part (c) above, in order to maximize its expected after-tax income? (Assume for simplicity that it cannot buy both insurance and Loss Control, but mut buy either only one of them or neither of them.) I (d) (9 pts) Suppose a different company offers Ludo Corporation a Loss Control service which costs S (in dollars) and which cuts the probability of all losses in half (such that the probability of both the small loss and the large loss are reduced to 1/6 rather than 1/3), meaning that the new probability distribution for the Ludo Corporation's pre-tax income is given by 100 S with prob. 2/3 70 - S with prob. 1/6 20 S with prob. 1/6 For what values of S will Ludo Corporation prefer to buy the Loss Control service instead of doing what you concluded it would do in part (c) above, in order to maximize its expected after-tax income? (Assume for simplicity that it cannot buy both insurance and Loss Control, but mut buy either only one of them or neither of them.)