Michelle received an inheritance of $95,000, and she is evaluating two speculative investments - the purchase of land and the purchase of cattle. Each investment would be for 1 year. Under "normal" economic conditions, each dollar invested in land will return the principal plus 20% of the principal; each dollar invested in cattle will return the principal plus 30%. However, both investments have some risk. If economic conditions were to worsen, there is an 18% probability she would lose everything she invested in land and a 30% probability she would lose everything she invested in cattle. Michelle does not want to lose more than $20,000 (on average). She wants to know how to allocate her investments to maximize the cash value of the investments at the end of 1 year.

a. Algebraically formulate this linear programming problem (6 marks)

b. Solve this problem using Excel. (6 marks)