运筹学作业代做 MATH3205代写 Operations Research代写

Homework #1 for MATH3205 Operations Research I

运筹学作业代做 Please submit your solutions to the HKBU moodle under Math3205 HW1. Problem 1. (20 marks) A family in Hong Kong requires 6 million dollars to

Please submit your solutions to the HKBU moodle under Math3205 HW1.

Problem 1. (20 marks)

A family in Hong Kong requires 6 million dollars to finance a new home, and three different banks have agreed to supply all or part of this amount. Although each bank insists that the loan plus interest charges be repaid over 6 years, the repayment schedules differ from bank to bank, as shown in the following table.

The family feels that it is advantageous to borrow in such a manner that the total yearly payments on the loan are as nearly as equal as possible, yet it does not wish to pay more than 4 million dollars in total interest charge. Set up a linear programming model that will determine the amount of money to be borrowed from each bank, such that the family’s objectives are realized.

Problem 2. (20 marks) Consider the following problem 运筹学作业代做

max z = 2x₁ + x₂ 

s.t. x₁ − 1 ≤ |x₂ − 1|,

x₁ ≤ 2,

x₂ ≤ 2,

x₁, x₂ ≥ 0.

Is the above problem an LP problem? If yes, convert it into our standard form. If no, prove it.

Problem 3. (20 marks) Consider the following problem

max {x₁, x₂}

s.t. x₁ + x₂ ≤ 1

x₁ ≥ 0, x₂ ≥ 0.

Is the above problem an LP problem? If yes, convert it into our standard form. If no, prove it.

Problem 4. (20 marks) 运筹学作业代做

HKBU Mathematics Society plans to organize a team competition from HKBU to Hong Kong Airport (about 33 kilometers). Each team has n students but with only one single-seat bicycle. Each member in the team must travel a distance of 33 kilometers from the same starting point to the same end point. For member j in the team, j = 1, · · · , n, the walking speed is w_j and the bicycling speed is b_j . Each team can arrange which member can ride the bicycle and can ride for how long or how far. The team clock is the time of the last person in the team reaches the ending point.

(a) Formulate this problem as a solvable mathematical problem.

(b) Is your mathematical problem established in (a) an LP problem? If yes, please convert into our standard form. If no, prove it.

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