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# Linear Programming- Thompson Distributors

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Thompson distributors packages and distributes industrial supplies. A standard shipment can be packaged in a class A container, a class K container, or a class T container. A single class A container yields a profit of \$6; a class K container, a profit of \$10; and a class T, a profit of \$8. Each shipment prepared requires a certain amount of packing material and a certain amount of time.

Formulate and solve this problem using LP software.4

Decision Variable:
X1=number of class A containers to be used
X2= number of class K containers to be used
X3= number of class T containers to be used

Resources needed per Standard Shipment

Class of container Packing Material (pounds) Packing Time (Hours)
A 2 2
K 1 6
T 3 4

Total amount of resource 180 pounds 240 hours
available per week

Jason Thompson, head of the firm, must decide the optimal number of each class of container to pack each week. He is bound by the previously mentioned resource restrictions but also decides that he must keep his 6 full-time packers employed all 240 hours (6 workers x 40 hours) each week.

Objective Function:
Minimize Z = ________
Select from choices below
A) X1 + X2 + X3
B) 180X1 + 240X2 or
C) \$6X1 + \$10X2+ \$8X3

Subject to: ___________ (Packing material)
Select from choices below
A) 2X1+1X2+3X3<180
B) X1+X2+X3<180 or
C) 2X1+1X2+3X2>180
X1, X2, X3 &#8805; 0
__________ (Packing Time)
Select from choices below
A) 2X1+6X2+4X3<240
B) 2X1+6X2+4X3>240 or
C) X1+X2+X3<240
X1, X2, X3 &#8805; 0

The optimal solution obtained by solving using LP software:

Number of class A containers to be used (X1) =_______ (Round your response to two decimal places).
Number of class B containers to be used (X2) = _______ (Round your response to two decimal places).
Number of class C containers to be used (X3) = ________ (Round your response to two decimal places).

Total profit (Z) = _________ (Round your response to two decimal places).

#### Solution Preview

Thompson distributors packages and distributes industrial supplies. A standard shipment can be packaged in a class A container, a class K container, or a class T container. A single class A container yields a profit of \$6; a class K container, a profit of \$10; and a class T, a profit of \$8. Each shipment prepared requires a certain amount of packing material and a certain amount of time.

Formulate and solve this problem using LP software.4

Decision Variable:
X1=number of class A containers to be used
X2= number of class K containers to be used
X3= number of class T containers to be used

Resources needed per Standard Shipment

Class of container Packing Material (pounds) Packing Time (Hours)
A 2 2
...

#### Solution Summary

Linear programming for Thompson Distributors are examined. The resources needed per standard shipments are examined.

\$2.19

## Linear Programming Modeling

A Brokerage firm has just been instructed by one of its clients to invest \$250,000 for her money obtained recently througn the sale of land holdings in Ohio. The client has a good deal of trust in the investment house, but she also has her own ideas about the distribution of the funds being invested. In particular, she requests that the firm select whatever stocks and bonds they believe are well rated, but within the following guidelines: a) Municipal bonds should constitute at least 20% of the investment. b) At least 40% of the funds should be placed in a combination of electronic firms, aerospace firms, and drug manufacturers. c) No more than 50% of the amount invested in municipal bonds should be placed in a high-risk, high-yield nursing home stock. Subject to these restraints, the client's goal is to maximize projected return on investments. The analysts at the brokerage firm, aware of these guideline, prepare a list of high-quality stocks and bonds and their corresponding rates of return:

Investment Protected Rate of Return %

Los Angeles municipal bonds 5.3
Thompson Electronics, Inc. 6.8
United Aerospace Corp 4.9
Palmer Drugs 8.4
Happy Days Nursing Home 11.8

a) Formulate this portfolio selection problem using LP.
b) Solve this problem.

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