1. [25 marks] A plane manufacturing company is considering four types of planes: jumbo, large, medium, and small. The resource required for and the profit for each type of plane are given below (Table 1):
Right now, the company has 7000 tons of steels, 60,000 assembler hours and 40000 engineer hours available. If the company decides to produce any type of plane, at least 100 planes of that type should be produced.
Formulate the corresponding integer programming problem to help the company decides how much if any of the planes should be produced.
an appropriate and comprehensive discussion on the
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Incorporate the following additional restrictions into your integer program:
a) ¡°If any large plane is to be produced, then small planes should be produced too, but no medium planes should be produced.¡± Solve the problem for the optimal schedule of planes. Comment on the solution.
b) ¡°Each unit of Jumbo plane that is produced over 100 units, requires a production time of 70 assembler-hours instead of 60 man-hours (e.g., producing 101 units of Jumbo plane requires 100(60) + 1(70) man-hours).¡± Solve the problem for the optimal schedule of planes. Comment on the solution.
c) ¡°If both Jumbo and medium planes are produced, 17,500 assembler-hours are needed for production line set-up and hence the (effective) number of assembler-hours available falls to 60000-17500=42500.¡± Solve the problem for the of on the solution.
Steel required
Assembler hours
Engineer hours
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