Mars One is an organization which aims to establish a permanent human settlement

Question

Mars One is an organization which aims to establish a permanent human settlement on Mars. You are one of the advisors of the Mars One team and you are trying to decide what you should carry with your spaceship to Mars. There are several items on your list, and your team assigned a value for each item. Unfortunately, you cannot take all the items in this list due to the limited capacity of the spaceship. You know the capacity of the spaceship as well as how much each item weighs. Your task is to maximize the total value of items carried to Mars under the capacity restriction. Formulate this problem as an integer program by (a) identifying the sets and parameters, (b) identifying the decision variables, (c) writing down the objective function using your notation from (a) and (b), (d) writing down the constraints using your notation from (a) and (b). (e) Explain the objective function and constraints in your formulation with 2-3 sentences.

Explanation / Answer

a) Below are the parameters -

Vi- Value of item i

Wi - Weight of item i

C - Capacity of space ship

b) The decision variables of the items include -

Xi = 0 or 1 (0 if the item is not carried and 1 if the item is carried)

c) Objective function -

Maximize the value of the items -

Z = Vi*Xi  

d) Below is the constraint for capacity -

Wi*Xi  <= Ci

e) Objective function multiples the value of each item with decision variable either 0 or 1 which gives the total maximum value of the items carried to Mars.

Constraint equation multiplies the weight of each item with decision variable either 0 or 1 which gives the total capacity of the items which should be less than or equal to the overall total capacity.

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