Question

Leach Distributors packages and distributes industrial supplies. A standard shipment can be packaged using a mix of class A, class K, and class T containers. A shipment in a single class A container yields a profit of $180; in a single class K container, a profit of $70; and in a single class T container, a profit of $150. Each container requires a certain amount of packing material as well as packing time, as shown below.

RESOURCES REQUIRED PER CLASS OF CONTAINER
Class of Container	Packing Material (Pounds)	Packing Time (Hours)
A	3	1
K	1	6
T	3	4

Hugh Leach, head of the firm, must decide the optimal number of each class of container to use for his weekly shipment. Each week, his supplier can supply him with 128 pounds of packing materials; additionally, each of his six full-time packers provides 40 hours of labor. Finally, Hugh has 25 class A, 14 class K, and 34 class T containers available to him each week.

Part A: Explicitly provide the following aspects of the problem in business terms:

• Goal/objective
• Decisions to be made
• Operational constraints

Part B: What quantitative model would be most appropriate to solve this problem?

Part C: Formulate and solve this problem using Excel.

Part D: Present the solution in Part C in terms of the business formulation you provided in Part A.

Answer 1

Part a:

• Goal/objective: Maximize the complete benefit for the firm.
• Decisions to be made: Number of containers of each class to be utilized every week.
• Operational constraints: Packing materials and time

Part b:

Linear programming model is the most suitable to solve this issue.