A 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. 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. xx Wall shelves sell for $29.95 and have a unit cost of $17.95; bookends sell for $11.95 and have a unit cost of $4.95; a shadow box sells for $16.95 and has a unit cost of $8.95.
some information is given in minutes, some in hours
a. Define are the decision variables, and state the linear programming model for the problem (objective function, constraints, etc.).
b. Implement and solve the model in Excel. Generate the sensitivity report. State your solution.
c. Which constraints are binding and which constraints have extra capacity? How much?
d. Identify the range of optimality for each objective function coefficient.
e. If the power saw were available for 40 hours, will the shadow price for that constraint change? Use the sensitivity report to answer the question.