There is two questions based on the information given

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• There is two questions based on the information given.
• The copyable version of chart is down below.

Investment	Projected Rate of Return (%)	Risk
Municipal bonds	5.2	Low
Real estate stock	10.5	High
Pharmaceutical stock	8.2	Moderate
Domestic automobile stock	8.4	Moderate

A brokerage firm has been tasked with investing $800,000 for a new client with the following guidelines:

1. At least 21% of the total amount invested should be in municipal bonds
2. No more than 50% of the total amount invested should be in real estate stocks.
3. The return from moderate-risk investments must be at least 30% of the return from high-risk investment.
4. At least 12% in pharmaceutical stock.

The client's goal is to maximize the return on investments.

The broker has prepared a list of high-quality stocks and bonds and their corresponding rates of return as shown in the table above.

Question 1:What is the optimal solution to this LP problem? 

Question 2:) Would the optimal solution change if the rate of return from Pharmaceutical stocks investment decreases to 8.0% and all other rates of return are unchanged? Explain.

Copyable version of Chart:

Investment

Municipal bonds

Real estate stocks

Pharmaceutical stocks

Domestic automobile stocks

Projected Rate of Return (%)

5.2

10.5

8.2

8.4

Risk

Low

High

Moderate

Moderate