Name: Prexy Ann Verola
Date: February 12, 2021
Due: Feb 15
Assignment: Linear Programming-Minimization
Write the linear program of the given problem:
The New Generation Power Corporation (Minimization Problem Graphical Method)
The main generator of the New Generation Power corporation burns two types of
fuel: Low sulfur and high sulfur, to produce electricity. For one hour, each
gallon of low sulfur emits 30 units of sulfur dioxide, generates 40 kilowatts
of electricity and costs P600. Each gallon of high sulfur emits 50 units of
sulfur dioxide, generates 40 kilowatts of electricity, and costs P500. The
environmental protection agency insists that the maximum amount of sulfur
dioxide that can be emitted per hour is 150 units. Suppose that at least 160
kilowatts of electricity must be generated per hour, how many gallons of low
sulfur and how many gallons of high sulfur must be utilized per hour in order
to minimize the cost of fuel.
Let x be the amount of low sulfur fuel
Let y be the amount of high sulfur
Objectives:
Minimize Cost:
C = 600x + 500y
1st Constraint
Subject to
S02: 30x + 50y ≤ 150
Electricity: 40x + 40y ≥ 160
X, Y ≥ 0
X
0
5
2nd Constraints
Y
3
0
X
0
4
Y
4
0
Linear Programming-Minimization
Solution:
C1: 30𝑥 + 50𝑦 = 150
= 30x = 150 – 50y
=
30𝑥
30
=
150−50𝑦
= 𝑥=5 −
30
5𝑦
C2: 40x + 40y = 160
=
40 ( 5 −
=
200 −
= 200 −
3
= −
x= 2.5
y= 1.5
80𝑦
3
=
80𝑦
−
3
=
−80𝑦
3
−80
3
5𝑦
3
200𝑦
3
80𝑦
3
) + 40𝑦 = 160
+ 40𝑦 = 160
= 160
= 160 − 200
= −40
=
y = 1.5
−40
−80
3
𝑥=5 −
𝑥 =5−
𝑥 = 2.5
5𝑦
3
5 (1.5)
3
FINAL SOLUTION
Objectives:
Minimize Cost:
C = 600x + 500y
= 600 ( 2.5 ) + 500 (1.5)
x= 2.5
y= 1.5
= 2,250
Let x be the amount of low sulfur fuel
Let y be the amount of high sulfur
= 30(2.5) + 50(1.5) ≤ 150
= 75 + 75 ≤ 150
Therefore, there should be 75 gallons of low sulfur and 75 gallons
of high sulfur that must be utilized per hour in order to minimize the cost of
fuel which is ₱2,250.