Introduction to Management Science 12th Edition by Bernard Taylor

Exercise 15

Solve the linear programming model formulated in Problem for Alexis Harrington by using the computer.
a. If Alexis decided to invest some of her own savings along with the money from her inheritance, what return would she realize for each dollar of her own money that she invested How much of her own savings could she invest before this return would change
b. If the risk of losing the investment in land increased to 30%, how would this change the optimal investment mix
Problem
Alexis Harrington received an inheritance of $95,000, and she is considering two speculative investments-the purchase of land and the purchase of cattle. Each investment would be for 1 year. Under the present (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 are relatively risky. If economic conditions were to deteriorate, there is an 18% chance she would lose everything she invested in land and a 30% chance she would lose everything she invested in cattle. Alexis does not want to lose more than $20,000 (on average). She wants to know how much to invest in each alternative to maximize the cash value of the investments at the end of 1 year.
Formulate a linear programming model for this problem.