D. Set up the initial simplex matrix needed to solve the liner programming problem using the simplex method E. Perform all pivots necessary using row operations to transfer the matrix until the solution is feasible F. How much should he invest in each to maximize his return, assuming investment returns are as expected ### Problem 4: Investment AllocationAn investor is considering three types of investments:1. **High-risk venture**: Oil leases with a potential return of 15%.2. **Medium-risk investment**: Bonds with a 9% return.3. **Relatively safe investment**: Stock investment with a 5% return.The investor has $50,000 to invest. Due to risk considerations, the following limitations are imposed:- Investment in oil leases and bonds is limited to 30%.- Investment in oil leases and stock is limited to 50%.**Objective**: Determine the investment strategy that maximizes returns, assuming investment returns are as expected.#### a. Define the Variables- $ x = $ Amount invested in oil leases.- $ y = $ Amount invested in bonds.- $ z = $ Amount invested in stocks.#### b. State the ConstraintsClearly define all constraints related to the feasible region using inequalities:- $ x + y + z = 50,000 $ (Total investment)- $ x + y \leq 0.3 \times 50,000 $ (Oil leases and bonds investment limit)- $ x + z \leq 0.5 \times 50,000 $ (Oil leases and stocks investment limit)- $ x, y, z \geq 0 $ (Non-negativity constraint)#### c. State the Objective FunctionThe objective function is the equation that needs to be maximized to find the optimal investment strategy:- Maximize $ 0.15x + 0.09y + 0.05z $ This objective function represents the expected return from investments in oil leases, bonds, and stocks, respectively.

Answered: a. Define the variables. Be specific…

a. Define the variables. Be specific with descriptive words. b. Clearly state the constraints (all inequalities) related to the feasible region. c. State the objective function.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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