Linear Programming : Sensitivity analysis and interpretation

Use Excel

Investment Advisors, Inc., is a brokerage firm that manages stock portfolios for a number of clients. A particular portfolio consists of U shares of U.S. Oil and H shares of Huber Steel. The annual return for U.S. Oil is $3 per share and the annual return for Huber Steel is $5 per share. U.S. Oil sells for $25 per share and Huber Steel sells for $50 per share. The portfolio has $80,000 to be invested. The portfolio risk index (0.50 per share U.S. Oil and 0.25 per share for Huber Steel) has a maximum of 700. In addition, the portfolio is limited to a maximum of 1000 shares of U.S. Oil. The linear programming formulation that will maximize the total annual return of the portfolio is as follows:

Max z = 3U + 5H

Subject to:

25U + 50H ≤ 80,000 Funds available

0.50U + 0.25H ≤ 700 Risk maximum

1U ≤ 1000 U.S. Oil maximum

U, H ≥ 0

Solve the problem using Excel Solver.

a) What is the optimal solution, and what is the value of the total annual return?

b) Which constraints are binding? What is your interpretation of these constraints in terms of the problem?

c) What are the shadow prices for the constraints? Interpret each.

d) Would it be beneficial to increase the maximum amount invested in U.S. Oil? Why or why not?

Solution Preview

Hello

See below for help and excel sheet for solution

a) What is the optimal solution, and what is the value of the total annual return?
Buy 800 of US oil shares and 1200 of Huber shares. Optimal total return is 8400

b) Which constraints are binding? What is ...

Solution Summary

The excel file contains Optimal solution and interpretation of solution. Excel solver tool is used to solve the problem.

This is a problem related to linearprogrammingandsensitivityanalysis.
Please solve this and explain how you arrived at the solution.
Please do this in Excel by using "Solver" or management science software...which ever is convinient for you.
The problem is attached.
Thank you.

LinearProgramming: SensitivityAnalysisandInterpretation of Solution
Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and grinder. The times (in minutes) required on each machine are as follows:
Machine
Component Shaper Grinder
1

A linear program has the objective of maximizing profit = 12X + 8Y. The maximum profit is $8,000. Using a computer we find the upper bound for profit on X is 20 and the lower bound is 9. Discuss the changes to the optimal solution (the values of the variables and the profit) that would occur if the profit on X were increased to

16. In a linearprogramming problem, the binding constraints for the optimal solution are
5X + 3Y < 30
2X + 5Y < 20
a. Fill in the blanks in the following sentence:
As long as the slope of the objective function stays between ____ and ___, the current optimal solution point will remain optimal.
b. Which of these

PLEASE EXPLAIN YOUR ANSWERS (why did you choose T instead of F or A instead of C, etc.).
C 1. Which of the following is not a component of the structure of a linearprogramming model?
a. parameters
b. decision variables
c. environment of certainty
d. constraints
F 2. In a linearprogramming model, the numb

PLEASE EXPLAIN YOUR ANSWERS (why you choose A instead of C, etc.).
C 6. For a resource constraint, either its slack value must be _____ or its shadow price must be ________
a. negative, negative
b. negative, zero
c. zero, zero
d. zero, negative
D 7. For a linearprogramming problem, assume that a given

Solve the linearprogramming model developed in Problem 22 for the Burger Doodle restaurant by using the computer. a. Identify and explain the shadow prices for each of the resource constraints. b. Which of the resources constraints profit the most? c. Identify the sensitivity ranges for the profit of a sausage biscuit and the a

Bradley Family
(a) Let X1 = # of acres of corn and X2 = # of acres of tobacco
Corn Tobacco Resources Available
300 520
Land 1 1 <= 410
Budget 105 210 <= 52500
Govt. Restriction 0 1 <= 100 Government Restriction
X1 X2
Decisio