Introduction to Management Science 12th Edition by Bernard Taylor

Exercise 11

Solve the linear programming model formulated in Problem for Alexis Harrington graphically.
a. How much would the return for cattle have to increase in order for Alexis to invest only in cattle
b. Should all of Alexis's inheritance be invested according to the optimal solution
c. How much "profit" would the optimal solution earn Alexis over and above her investment
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.