Leach 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 container, 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. Decision variables: 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 available per week 180 pounds 240 hours Hugh Leach, 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 × 40 hours) each week. Objective function: Maximize Z = $ 6 Upper X 1 plus $ 10 Upper X 2 plus $ 8 Upper X 3$6 X1+$10 X2+$8 X3 Subject to: 2 Upper X 1 plus 1 Upper X 2 plus 3 Upper X 3 less than or equals 1802 X1+1 X2+3 X3 ≤ 180 (packing material) 2 Upper X 1 plus 6 Upper X 2 plus 4 Upper X 3 equals 2402 X1+6 X2+4 X3=240 (packing time) X1, X2, X3≥0

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 107P

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Related questions

Question

Leach 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 container, 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.

Decision variables:

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 available per week	180	pounds	240	hours

Hugh Leach, 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

full-time packers employed all

240

hours

workers

hours) each week.

Objective function:

Maximize Z =

$ 6 Upper X 1 plus $ 10 Upper X 2 plus $ 8 Upper X 3$6 X1+$10 X2+$8 X3

Subject to:

2 Upper X 1 plus 1 Upper X 2 plus 3 Upper X 3 less than or equals 1802 X1+1 X2+3 X3 ≤ 180

(packing material)

2 Upper X 1 plus 6 Upper X 2 plus 4 Upper X 3 equals 2402 X1+6 X2+4 X3=240