Logic Controller Corp. $($LCC$)$ is a global programmable logic controller manufacturer. It divides its worldwide market into five regions: $(1)$ North America, $(2)$ South America, $(3)$ Asia, $(4)$ Europe, and $(5)$ Africa. The annual demands for these five regions are $128,000,110,000,169,000,111,000,$ and $78,000$ units, respectively. It has determined that a manufacturing plant should have an annual capacity of $200,000$ units. The fixed annual costs of maintaining such a manufacturing plant in the five regions are $$60$ million, $$45$ million, $$50$ million, $$55$ million, and $$40$ million, respectively. The costs $($including production, inventory, transportation, and tariffs$)$ of supplying one controller from a facility location to a market are shown below.

Facility

North America

South America

Asia

Europe

Africa

North America

$200$

$210$

$225$

$220$

$220$

South America

$190$

$180$

$205$

$205$

$200$

Asia

$195$

$200$

$180$

$190$

$190$

Europe

$215$

$210$

$210$

$200$

$205$

Africa

$180$

$185$

$190$

$190$

$170$

Based on three scenarios answer the questions below and support your answer. Use data analysis solver Simplex LP in Excel to help answer the questions.

Scenario $1.$

Using the data provided, how can the company minimize its facility and supply cost?

What is the lowest cost solution for adding a new plant, its location, and how many?

Scenario $2.$

Using the data provided and that one plant must be built in North America, how can the company minimize its facility and supply cost?

What is the lowest cost solution for adding new plants, its location, and how many?

Scenario $3.$

Using the data provided and that one plant must be built in each of the five regions, how can the company minimize its facility and supply cost?

What is the lowest cost solution for adding new plants, its location, and how many?