can u please solve this question

Suppose u(W) = In W for an agent. The agent faces the following gamble: with probability 0.5 wealth is 100, and with probability 0.5 a loss occurs so that wealth becomes 64. The agent can buy any amount of insurance: a coverage of X can be purchased by paying premium rX. (a) Work out the insurance coverage X that the agent would optimally purchase as a function of r. (b) Plot the optimal X as a function of r. (c) Calculate the value of r for which full insurance is purchased. (d) Calculate the value of r for which no insurance is purchased