I. This case is worth 10% of the course total grade.

2. This case is to be solved indin’dually.

3. Students cheating solutions fiom each other or plagiarizing answers from any other
source will be awarded a grade of zero for the case. There is zero tolerance policy
when it comes to plagiarism.

4. The case is due on MondayI June 1″i 2015 and it is to be submitted during class.

5. The developed linear program shall be solved using both Excel Solver as well as
LINGO software.

6. Include a hard copy of the Excel sheet and the LINGO code with your report along
with a hard copy of the output report generated by both Excel and Lingo after running
the code.

W The ACM Comp-1n.“

The Arabian Carpet Manufacturing (ACM) Company is one of the leading carpet producers
in the region. Competition in this industry is intense and forces producers to strive for maximum
efliciency and economies of scale. It also forces producers to continually evaluate investments in
new technology. As such the owner of the ACM Company is seeking your assistance in
planning the production schedule for the next quarter (13 weeks). The company has orders for
fifieen difierent types of carpets that the company can produce on two types of looms: Dobbie
looms and Pantera looms. Pantera looms produce standard tufted carpeting. Dobbie looms can
also produce standard tufied carpeting but also allow the incorporation of designs (such as
flowers or corporate logos) into the carpeting.

The following table summarizes the orders for each type of carpet that must be produced in
the coming quarter along with their production rates and costs on each type of loom, and the cost
of subcontracting each order. Note that the first 4 orders involve special production requirements
that can only be achieved on a Debbie loom or via subcontracting. Assume that any portion of an
order may be subcontracted.

cm Demand

we ms)

m-

m.

um

um-
ACM currently owns and operates 15 Dobbie looms and 80 Pantera looms. In order to

maximize efiiciency and keep pace with demand the company operates 24 hours a day, 7 days a

week Each machine is down for routine maintenance for approximately 2 hours per week.

Managerial Report

a) Formulate the above problem as a linear program (LP). Clearly define the decision
variables and provide a verbal description of the objective function as well as each of the
constraints.

b) Solve the model developed in part (a) using Excel solver.

c) Solve the model developed in part (a) using LINGO.

d) What is the optimal production plan obtained, and what is the associated optimal
objective function value?

9) Is the optimal solution obtained degenerate? Why?

1′) Is the optimal solution obtained unique? Why?

g) Comment on the utilization of the resources (i.e., which of the resources have been fully
utilized and which haven‘t).

h) Discuss the range of optimality for the objective function coefficients and provide its
interpretation.

i) Discuss the range of feasibility for the constraints right hand sides and provide its
interpretation.

j) Present the shadow prices for the constraints along with their interpretations.

k) If ACM wanted to decrease the production of any carpet type, which one would you
recommend and why? (assume minimum production requirement could be violated)