Wood Specialties Company Produces Wall Shelves, Bookends, and Shadow Boxes

question 29

Essay

Wood Specialties Company produces wall shelves, bookends, and shadow boxes. It is necessary to plan the production schedule for next week. The wall shelves, bookends, and shadow boxes are made of oak, of which the company has 600 board feet. A wall shelf requires 4 board feet, bookends require 2 board feet, and a shadow box requires 3 board feet. The company has a power saw for cutting the oak boards into the appropriate pieces; a wall shelf requires 30 minutes, bookends require 15 minutes, and a shadow box requires 15 minutes. The power saw is expected to be available for 36 hours next week. After cutting, the pieces of work in process are hand finished in the finishing department, which consists of 4 skilled and experienced craftsmen, each of whom can complete any of the products. A wall shelf requires 60 minutes of finishing, bookends require 30 minutes, and a shadow box requires 90 minutes. The finishing department is expected to operate for 40 hours next week. Wall shelves sell for $29.95 and have a unit variable cost of $17.95; bookends sell for $11.95 and have a unit variable cost of $4.95; a shadow box sells for $16.95 and has a unit variable cost of $8.95.
(A) Is this a problem in maximization or minimization?
(B) What are the decision variables? Suggest symbols for them.
(C) What is the objective function?
(D) What are the constraints?

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Definitions:

Utilization Factor

A metric that measures the percentage of time that a resource (e.g., machine, employee) is actively used compared to the total available time.

Time Between Arrivals

The average or specified period of time that elapses between the arrival of successive units, customers, or entities in a process or system.

Repetitive Focus Factory

A factory designed to produce high volumes of a limited range of products, focusing on efficiency and repetitive processes.

Processing Part

The phase or component in manufacturing that involves the change or transformation of materials into final products.