Provide a Linear Programming Model (in both algebraic and spreadsheet formats) for the above case. You model should clearly state the Decision Variables, objective function, and constraints.

(b) Use SOLVER module on Microsoft Excel to solve your model in part (a) and interpret your results.

A joint GCC Company manufactures and distributes meters used to measure electric power consumption. The company started with a small production plant in Musafah and gradually built up a customer base throughout the region through a distribution center in Khalifa Industrial Zone in Abu Dhabi (KIZAD). Later when business expanded, Jabal Ali in Dubai was used as a second distribution center. The Musafah plant was expanded when the company began marketing its meters in other GCC countries. With the growth of the business, the Company opened a third distribution center in Dammam, KSA. The company pays a quarterly fixed admin cost for utilizing the distribution centers as follows: $40,000 in Kizad, $35,000 in Jabel Ali, and $30,000 in Dammam. Just two years ago opened a second production plant in Ras Al Khaimah (RAK). Manufacturing costs differ between the company's production plants. The cost of each meter produced at Musafah plant is $10.50. The RAK plant utilizes newer and more efficient equipment; as a result, manufacturing costs are $0.5 per meter less than the Musafah plant. Due to the company's rapid growth, not much attention has been paid to the efficiency of the distribution system, and management has decided it is time to address this issue. As noted above, there are two plants and three distribution centers. The cost of shipping a meter from each plant to each distribution center, given in dollars is shown below. Plant Musafah RAK Distribution Centers Damam KIZAD Jabal Ali 3.2 2.2 | 4.2 -- I 3.9 1.2 The Quarterly production capacity is 30,000 meters at the older Musafah plant and 20,000 meters at the RAK plant. Note that no shipments are allowed from the RAK plant to the Damam distribution center. The company serves nine customer zones from the three distribution centers. The forecast of the number of meters needed in each customer zone for the next quarter is shown below. Customer Zone Dhahran Manama Riyadh Kuwait Jeddah Salala Muscat Nizwa Sohar Demand 6300 4880 2 1301210 6120 4830 2750 85804460 The per-unit costs of shipping from each distribution center to each customer zone are given in dollars in the table below; note that some of the distribution centers cannot serve certain customers zones. Sohar Jeddah Salalah Center Damam Dhahran 0.3 5.2 Manama 2.1 5.4 Riyadh 3.1 4.5 Customer Zones Kuwait Muscat Nizwa 4.4 6.0 -- 6.0 2.7 4.7 5.4 3.3 | 3.4 2.4 3.3 2.1 2.7 2.5 Jabal Ali In the current distribution system, demand at the Dhahran, Manama, Riyadh, and Kuwait customer zones is satisfied by shipments from Damam distribution center. In a similar manner, the Muscat, Nizwa, and Sohar customer zones are served by the KIZAD distribution center. In addition, the Jeddah and Salalah customer zones are covered by Jabel Ali distribution center. To determine how many units to ship from each plant, the quarterly demand forecasts are aggregated at the distribution centers, and a transportation model is used to minimize the total costs (fixed + production + transportation) of shipping from the production plants to the distribution centers