Michelle received an inheritance of $95,000, and she is evaluating two speculati
ID: 3135966 • Letter: M
Question
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 principle plus 20% of the principle; each dollar invested in cattle will return the principle plus 30%. However both investments have some risk. If economic conditions worsen, there is an 18% probability theat she will 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 investment to maximize the cash value of the investments at the end of 1 year.
Algebraically formulate this linear programming problem.
Explanation / Answer
Variable
x : investment in land
y : investment in cattle
Constraint
1. x and y >= 0
2. x+y <= 95000
3. 0.18x + 0.30 y <= 20000
Objective
Maximize investment+RoI
RoI + investment from land = x * 1.2 * 0.82 + x * 0 * 0.18 = 1.2*0.82 *x
{in 82% cases, the return on land will be 1.2 times the principal and in 18% it will be 0)
similar for cattle, RoI + investment = y* 1.3 *0.70 + y * 0 * 0.30 = 1.3*0.70*y
so maximize 1.2*0.82 *x + 1.3*0.70*y
solution
optimization suggest to invest everything in land.
variable x 95000 variable y 0 Constraint1 x and y >= 0 Constraint2 x+y <= 95000 0 Constraint3 0.18x + 0.30 y <= 20000 2900 objective maximize 1.2*0.82 *x + 1.3*0.70*y 93480