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 ≥ 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 ≥ 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).