Introduction to Operation Engineering Management Decision Analysis Product Mix Y

Introduction to Operation Engineering Management Decision Analysis
Product Mix
Your company is in construction business and is planning to build Houses (X1), Apartments (X2), and offices (X3).
a) The company has permission to build no more than a total of 10,000 units of the above structures.
b) A special type of iron bars are used for the foundation. Offices use twice that material than houses and apartments use three times of that material than houses. The company can source no more that 16,000 tons of this material.
c) The amount of wiring for internet and other communication needs in an office is 3 times that of a house and an apartment uses twice that amount of wire than a house. The company has no more than 15,000 meters of such wiring material.
d) Profit from each house is 3 million Rial, from an apartment is 5 million Rial and from an office is 4 million Rial
Question: Given the above constraints, how many houses, apartments, and offices should the company build to maximize its profit
1. Cast the above problem as a Linear Programming question
a) What is the objective function?
b) What are the constraints?
c) Is House = 5000, Apartments = 6000 , Offices = 7000
i. A solution
ii. A feasible solution
d) Give a solution of your own that is infeasible
Any values that violate at least one of the constraints is an infeasible solution for example
e) Is House = 1000, Apartments = 2000 , Offices = 3000
i. A solution
ii. A feasible solution
f) Give a solution of your own that is feasible
Any set of numbers that satisfy the constraints is a feasible solution for example
g) Using EXCEL to find the optimal feasible solution and the total profit in that cas
h) If the results of part g are not integers, let [x] be the largest integer ≤ x. For example [2.33] = 2. Replace results of optimal solutions by [x] and [x]+1 and indicate feasible solutions and the profit in each case.