Answer Happy

OPTION 2 A company is considering diverting production of three
products to a new manufacturing facility. All three products would
require production time at two machining centres in the facility
(i.e. not either/or, both centres are used). The products may be
produced in fractional amounts. The new facility has production
capacity restrictions, there is a maximum of 100 hours available at
each machining centre per week. The three products are produced
from two raw materials which cost €0.60 and €0.80 respectively per
kilogram used and can be sourced without restriction. The table
below provides further relevant data.
123Revenue per unit (€)232.55Maximum demand (units)100200100Time
required per unit in MC 1 (hours)0.50.81Time required per unit in
MC 2 (hours)0.80.60.2Qty of Raw Material A required per unit
(kg)0.10.20.075Qty of Raw Material B required per unit
(kg)0.050.10.05Product
The lead engineer for the new product introduction project has
developed the following Linear Programming model to assist with the
decision-making processes.
max𝑧 = 2X1+3X2+2.55X3−0.6𝑅1−0.8𝑅2
Subject to
0.5X1+0.8X2+X3≤100
0.8X1+0.6X2+0.2X3≤100
X1≤100,X2≤200,X3≤100
𝑥1,𝑥2,𝑥3≥0
Where the quantity of each raw material used in the production
of these products are given by:
𝑅1=0.1𝑥1+0.2𝑥2+0.075𝑥3
𝑅2=0.05𝑥1+0.1𝑥2+0.05𝑥3
However, the industrial engineer has realised that the above LP
model does not reflect some important aspects that a model would
need to consider to be a useful decision-making tool: (a) The raw
material costs are nonlinear in the following fashion: • Raw
Material 1 (𝑅𝑅1): The unit cost for the first 50 kilograms is €0.60
per kg. The unit cost for amounts greater than 50 but less than 100
is €0.70 per kg. The unit cost for purchases above 100 kg. is €0.75
per kg. • Raw Material 2 (𝑅𝑅2): The unit cost for the first 50
kilograms is €0.80 per kg. The unit cost for amounts greater than
50 but less than 100 is €0.75 per kg. The unit cost for purchases
above 100 kg. is €0.70 per kg. • Note: these costs are
increasing/decreasing for the additional units, e.g. if 160kg of
Raw Material 1 are consumed, the first 50kg costs €0.60 per kg, the
next 50kg costs €0.70 per kg and the remaining 60kg costs €0.75 per
kg (b) The Sales Department have insisted that a logical
restriction is included in the model that if the company produce
more than 20 of product 1, then they must produce at least 5 of
product 2. 123Revenue per unit (€)232.55Maximum demand
(units)100200100Time required per unit in MC 1 (hours)0.50.81Time
required per unit in MC 2 (hours)0.80.60.2Qty of Raw Material A
required per unit (kg)0.10.20.075Qty of Raw Material B required per
unit (kg)0.050.10.05Product (c) The company’s senior management
have stipulated that production for at most of two of the three
products will be transferred to the new facility. Requirements: 1.
Develop a Mixed Integer Programming model that accounts for these
additional restrictions. 2. Transfer the model to Excel and use
Excel Solver to find a solution for the Industrial Engineer (i.e.
which products to produce, the quantities of the products to be
produced and the anticipated revenue for the company). NOTE: if you
prefer you can use another solution method (e.g. R or Python) but
it must be a computer based solution (no manual calculations). 3.
The report should be written to the same guidelines as provided in
the original assignment description document.