Leesa runs an organic farm in New York. Her daughter is about to give birth in Florida and Leesa wants to spend the summer with her grandchild. Leesa would like to hire Jasper to run the farm in her absence. However, Leesa has concerns about Jaspers work ethic and she is worried that he will not work hard enough in her absence. Leesa knows that if Jasper takes it easy, profits will be low with a probability of 60%, medium with a probability of 30% and high with the remaining probability. If Jasper puts out a medium level of effort, profits will be low with a probability of 40%, medium with a probability of 40% and high with the remaining probability. Finally, if Jasper works hard, profits will be low with a probability of 20%, medium with a probability of 40% and high with the remaining probability. Leesa also knows that Jasper will only take the job if his total expected pay is at least $4000; he will put in medium effort if doing so increases his expected pay by $1000 and he will work hard if doing so increases his expected pay by another $1200. Leesa agrees to pay a base salary of S that Jasper gets regardless of the profits. In addition, she offers him a bonus of if the profits are medium and a bonus of if the profits are high. Leesa wants to motivate Jasper to work hard at the lowest expected cost to herself. Write down the equations that Leesa must solve to find the values for S, , and that will allow her to achieve this goal. Bonus solve for those values.