Hide Folder Information

Instructions

A commercial printing firm is trying to determine the best mix of printing jobs it should seek, given its current capacity constraints in its four capital$-$intensive departments: typesetting, camera, pressroom, and bindery. It has classified its commercial work into three classes: A$,$ B$,$ and C$,$ each requiring different amounts of time in the four major departments. The production requirements in hours per unit of product are as follows:

Department

Class of Work

A

B

C

Typesetting

$0$

$2$

$3$

Camera

$3$

$1$

$3$

Pressroom

$3$

$6$

$2$

Bindery

$5$

$4$

$0$

Assuming these units of work are produced using regular time, the contribution to overhead and profit is $$200$ for each unit of Class A work, $$300$ for each unit of Class B work, and $$100$ for each unit of Class C work. The firm currently has the following regular$-$time capacity available in each department for the next time period: typesetting, $40$ hours; camera, $90$ hours; pressroom, $200$ hours; bindery, $160$ hours. In addition to this regular time, the firm could utilize an overtime shift in typesetting, which would make available an additional $35$ hours in that department. The premium for this overtime $($i$.$e$.,$ incremental costs in addition to regular time$)$ would be $$4/$hour$.$ Since the firm wants to find the optimal job mix for its equipment, management assumes it can sell all it produces. However, to satisfy long$-$established customers, management decides to produce at least $10$ units of each class of work in each time period.

A$.$ Define decision variables and formulate objective function$(2)$

B$.$ Constraints formulations$(2)$

C$.$ Solver Solution$(2)$

D$.$ Solution Interpretation:

Why is the shadow price of regular typesetting different from the shadow price of overtime typesetting?$(1)$

If the printing firm has a chance to sell a new type of work that requires $0$ hours of typesetting, $2$ hours of camera, $2$ hours of pressroom, and $1$ hour of bindery, what contribution is required to make it attractive?$(1)$