Subject: Statistics: Operational Analysis.

Homework: Linear programming modeling & solution I

1. (A production problem) The Mantell Company makes softballs and baseballs. In order to make each type of ball, leather, nylon, wood chips and machine time and labor are needed. The requirements for each item and the resources available are show in the following table:

Item

Softball

Baseball

Available

Leather

6 ounces

4

6000

Nylon

8 yards

3

5000

Wood Chips

10 ounces

2

5000

Labor

3 minutes

2

3600

Machine

1 minute

1

2000

Softballs sell for $17 each, and baseball sell for $15 each. Formulate & solve a linear programming model that can be used to determine the number of each type of ball to produce in order to maximize revenue.

1. (An investment problem) A client has approached a stockbroker with the following request: invest $100,000 for maximum annual income under 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 oil stock

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

Stock

Price/share

Estimate Annual return/share

Oil

$120

$11

Auto

$52

$4

Pharmaceutical

$18

$2

Formulate & solve a linear programming model to determine the investment so as to maximize the total estimated returns.