HW-Linear modeling

Setup a mathematical model with algebraic symbols for the two questions. Note that you do not have to build separate models for each of the sub questions. Instead, you can build the basic model to find the optimal solution first, and then answer each sub questions based on that model or some variations of that model.

Upload three (3) files: a Word document that contains your model and a descriptive answer to questions; an Excel file that contains your model implementation; and a script-explanation that walks through the logic of your solution.

Question 1

Momentoitalia.com is property of CGS Group Intl. Inc, an established company based in New

York City. It is 20 years that CGS represents Italian modern furniture companies in the USA. CGS

is working with all the major contemporary furniture stores, designers, architects, contractors and

private customers too. It started its activity by acting as a representative agent for some of the

major Italian lines such as B&B and Maxaalto, when Italian design was still a reality concentrated

to a small niche of the market. Momentoitalia.com have a wide selection of Italian bedroom

furniture and living room furniture and Italian sofas, sectionals and sofa beds.

Momentoitalia produces three types of sofas, which it sells to a variety of customers. The

production of each sofa requires two machine operations, trimming and shaping, followed by

assembly, which includes inspection and packaging. All three types require 4 hours of assembly

time, but the machining operations have difference processing times, as shown below, in hours per

unit:

Each machine is available 1000 hours per month, and the current size of the assembly department provides capacity of 1000 hours as well. Each sofa produced yields a unit profit contribution as follows:

1. Formulate a mathematical programming model that can help Momentoitalia to optimize its

performance. Your model should include clearly defined Parameters (Inputs), Objective,

Decisions, and Constraints.

 

1. Implement the model in excel and find optimal solutions.

 

1. If Momentoitalia could invest in additional machine hours on the Shaping operation, how much

would Momentoitalia be willing to pay for each additional hour obtained? Explain.

 

1. If the Assembly department adds additional 200 hours in capacity, how would Momentoitalia’s

optimal production plan change? Explain.

 

1. If Momentoitalia could invest in additional 100 machine hours, which machine should it invest

to increase the capacity. In other words, should it expand trimmer, shaper, or assembly hours first?

With this increased hour, how would Momentoitalia’s optimal production plan change? Explain.

Question

FedEx Freight is an LTL shipping industry leader that serves the U.S., Canada, Mexico, Puerto

Rico, and the U.S. Virgin Islands.

You were asked by the FedEx Freight to help with loading cargo ships at the Port of Los Angeles.

You have been asked to prepare a loading plan for a FedEx freighter bound for Puerto Rico. An

agricultural commodities dealer would like to transport the following products aboard this ship:

You can elect to load any or all of the available commodities. However, the ship has three cargo

holds with the following capacity restrictions:

More than one type of commodity can be placed in the same cargo hold. However, because of

balance considerations, the weight in the forward cargo hold must be within 10 percent of the

weight in the rear cargo hold, and the center cargo hold must be between 40 percent and 60 percent

of the total weight on board.

 

1. Formulate a mathematical programming model that can help FedEx Freight to optimize its

performance. (You can continue to next page for your formulation.) Your model should

include clearly defined Parameters (Inputs), Objective, Decisions, and Constraints.

 

1. Solve the above model in excel and find the optimal loading quantity.

 

1. How does your optimal loading plan change if the Profit per Ton for commodity 3 increases

from $60 to $70 per ton?

 

1. Likewise, would 𝑥 likely to increase or decrease if the Profit per Ton for commodity 1

decreases from $70 to $60 per ton? Explain.

 

1. Suppose FedEx Freight would like to expand its Cargo Hold capacity. If it costs FedEx Freight

$150 to expand Weight Capacity by a ton and $1 to expand Volume Capacity by a cu.ft., which

Cargo Hold should FedEx Freight expand first? Explain.

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