I need a detailed explanation and assistance to solve this proble: A client asks his stockbroker to invest $100,000 for maximum annual income, subject to the three conditions: Spread the investment over no more than three different stocks. Put no more than 40 percent of the money into any one stock Put a minimum of $10,000 into an oil stock. The broker has identified three stocks for investment.  Their estimated annual returns per share and price per share are shown in the following table:   Stock Price per Share Estimate Annual Return per Share Oil $120 $11 Auto $52 $4 Pharmaceutical $18 $2 The client wishes to use LP to determine the optimal number of shares to buy for each stock, so as to maximize the total estimated return. a) Write down the decision variables. b) Write down the optimization statement for the objective function. c) Write down the constraints.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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I need a detailed explanation and assistance to solve this proble:

A client asks his stockbroker to invest $100,000 for maximum annual income, subject to the three conditions:

  1. Spread the investment over no more than three different stocks.
  2. Put no more than 40 percent of the money into any one stock
  3. Put a minimum of $10,000 into an oil stock.

The broker has identified three stocks for investment.  Their estimated annual returns per share and price per share are shown in the following table:

 

Stock

Price

per Share

Estimate Annual Return

per Share

Oil

$120

$11

Auto

$52

$4

Pharmaceutical

$18

$2

The client wishes to use LP to determine the optimal number of shares to buy for each stock, so as to maximize the total estimated return.

a) Write down the decision variables.

b) Write down the optimization statement for the objective function.

c) Write down the constraints.

 

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