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Question: a new oil field has been discovered in the east...

Question details

A new oil field has been discovered in the east coast of Peninsular Malaysia. As an engineer for an oil exploration and extraction company, you have been assigned to determine the site to place the offshore oil platform. The topography of the seabed with the oil field can be represented by z x2 +xyty2, where z is the depth of seabed. Due to the weak economic growth and low oil prices, the installation area for the oil platform has been limited to a specific region, x2 y 8. Your experience taught you that the closer the distance between the oil platform and seabed, the lower the overall expenses. Hence, please propose a suitable location for the installation of oil platform within the designated region and with the lowest expense. Your solutions should include the following items: 2. i. new variables, ii. quadratic equation in matrix notation form, iii. eigenvalues and its corresponding eigenspaces, iv. orthogonal basis, v. constrained maximum and minimum as well as the corresponding locations. (20 marks)

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